New Place and Route Algorithms for Wire Length Improvement With Concern to Critical Paths

play.mvc中的route规则摘要：一、play.mvc 简介1.play.mvc 框架概述2.play.mvc 框架的优势二、route 规则概述1.route 规则的作用2.route 规则的基本语法三、route 规则示例1.静态路由示例2.动态路由示例3.参数传递示例四、route 规则高级应用1.路径参数和查询参数的区别2.路径参数的默认值3.路由别名与重载五、路由规则配置1.在application.conf 中配置路由规则2.在Java 代码中配置路由规则六、总结1.play.mvc 中route 规则的重要性2.route 规则在实际项目中的应用正文：play.mvc 是一个用于构建Web 应用程序的Java 框架，它提供了许多内置功能，如路由、模板引擎、安全等。

其中，路由是play.mvc 框架的核心功能之一，它可以帮助我们将URL 映射到特定的Controller 和方法。

在play.mvc 中，route 规则用于定义URL 与Controller 之间的映射关系。

它通过识别URL 中的特定模式，将请求转发到对应的Controller 和方法。

route 规则的基本语法如下：```scss/pattern1/:param1/:param2/:param3```其中，`pattern1`是URL 的模式，`param1`、`param2`和`param3`是URL 中的参数。

在实际应用中，我们可以根据需要定义不同的route 规则。

以下是一些route 规则示例：1.静态路由示例：```scss/hello controllers.Application.hello()```这个示例中，URL 为`/hello`时，将调用`controllers.Application`类的`hello()`方法。

2.动态路由示例：```scss/users/:id erController.show(id: Long)```这个示例中，URL 为`/users/1`时，将调用`erController`类的`show(id: Long)`方法，并将`id`参数的值传递给方法。

等价多路径间流量分配调度算法研究1 233林伟，刘斌，唐毅（1．清华大学深圳研究生院广东深圳 518055；2. 香港城市大学香港；3．清华大学计算机科学与技术系，北京 100084）lin-w04@摘要：为了减少网络拥塞并充分利用链路带宽，当在转发节点与目的子网间存在有多条等价路径（ECMPs）时，流量负载应该在ECMPs间均衡分配，并且属于同一个TCP流的IP分组应该按照相同顺序到达目的主机。

本文提出了一种基于LRU1 Cache和计数统计的算法。

该算法通过为每条ECMP分配一个计数器，利用计数统计从而考虑到了IP分组的长度差异。

使用相对计数以及对某些情况增加约束条件解决了计数器溢出问题。

UDP分组只需要作为调节负载均衡的流量。

更进一步，对于去往同一目的子网的不同主机的TCP流的时延差异被转化为cache中的表项失效的时间长度差。

仿真实验表明，当ECMPs间的时延差不显著的情况下，只需要很小的存储空间，且每次cache查找只需要一个时钟周期，负载均衡接近最优，此时只有2%的分组出现乱序。

关键词：流量分配；等价多路径；LRU；Cache；计数统计中图分类号：TP393.051 引言随着Internet网络规模的的迅速扩大，其拓扑结构日趋复杂。

从流量工程、可靠性和网络安全等因素考虑，网络中的两个节点间部署了多条路径。

目前，绝大部分单一路径路由协议都是基于dijkstra的最短路径算法，只有开销最小的路径被选为路由路径。

按照这种算法，网络所提供的带宽没有被充分利用，有可能出现多条路径中的一条路径负载过重，而其他路径却处于空闲状态，如此将造成网络的局部拥塞。

当IP分组经过多个节点之后，负载不均衡的情况可能会进一步加剧。

如果存在多于一条的路径的开销近似相等，单一路径路由协议的计算结果会在这几条路径间变化，造成频繁的路由表更新，网络变得不稳定，性能也受到影响[1]。

与单一路径路由协议不同，等价多路径路由协议被提出用以解决上述的问题[2, 3]。

Journal of the Chinese Institute of Engineers, Vol. 29, No. 6, pp. 945-952 (2006)945AN ALGORITHM TO BUILD CONVEX HULLS FOR 3-D OBJECTSHan-Ming Chen* and Tzung-Han LinABSTRACTIn this paper, a new algorithm based on the Quickhull algorithm is proposed to find convex hulls for 3-D objects using neighbor trees. The neighbor tree is the data structure by which all visible facets to the selected furthest outer point can be found.The neighboring sequence of ridges on the outer boundary of all visible facets also can be found directly from the neighbor tree. This new algorithm is twice as efficient as Barber’s algorithm.Key Words: 3-D convex hull, quickhull algorithm, computational geometry.*Corresponding author. (Tel: 886-2-23680375; Fax: 886-2-23631755; Email: hmchen@.tw)The authors are with the Department of Mechanical Engineering,National Taiwan University, Taipei, Taiwan 106, R.O.C.I. INTRODUCTIONThe convex hull of a set S of points is defined as the smallest convex set containing all the points in S. It is one of the most fundamental concepts in the field of computer graphics, computational geometry,pattern recognition, computer-aided design, image processing (Robert and Faugeras, 1995), and robotics.It also plays an important role in many applications such as shape determination (Kaasalainen and Torppa,2001), collision detection (Sherali et al ., 2001), find-ing the minimum bounding box (O’Rourke, 1993),and constructing spherical Voronoi diagram (Sugihara, 2000).Graham (1972) proposed an algorithm running in time complexity O (n log n ) for finding the convex hull of a set of planar points. Anderson reevaluated Graham’s algorithm for simplifying the computation to determine whether the second point in three con-secutive points is convex or not (Anderson, 1978).Later, several quick methods based on Graham’s al-gorithm were published to determine a 2-D convex hull for a set of planar points (Atwah et al ., 1995;Atwah and Baker, 2002; Koplowitz and Jouppi, 1978).Jarvis presented a convex hull identification method that includes point deletion checks and is especially effective when the number of points on the plane is relatively small (Jarvis, 1973). In 1996, an algorithm that is a parallel adaptation of Jarvis March and theQuickhull algorithm was presented by Atwah et al .(1996).In recent decades, at least four algorithms for finding the multi-dimensional convex hull have been proposed. They are gift wrapping, divide and conquer,incremental, and Quickhull algorithms (O’Rourke, 1993).Chand and Kapur (1970) first presented the gift wrapping algorithm in arbitrary dimensions. In the gift wrapping algorithm, the convex hull of a point set is generated by continuing to find the hyperplane making the maximum interior angle with the adja-cent facet until all facets found are closed. Assume that the number of points is n . The gift wrapping algorithm runs in time O (n 2). Sugihara revised the conventional gift wrapping algorithm to increase nu-merical robustness and topological consistency and kept the same time complexity as the conventional algorithm (Sugihara, 1994).The divide and conquer algorithm was first pro-posed by Preparata and Hong (1977) to apply a merge procedure for finding the convex hull of two non-in-tersecting convex hulls in two or three dimensions with O (n log n ) operations. A more detailed imple-mentation of the 3-D divide and conquer algorithm was presented by Day (1990).O’Rouke (1993) presented a detailed implemen-tation for the incremental algorithm. Initially, one tetrahedral hull is formed by randomly selecting four non-degeneracy points. Each time a new tetrahedron is formed with an outside point and a triangle on the old hull. Afterward this new tetrahedron is merged into the old hull and the concave parts of the merged hull are filled up. The incremental algorithm is some-times called the beneath-beyond algorithm. Allison946Journal of the Chinese Institute of Engineers, Vol. 29, No. 6 (2006)and Noga (1997) combined the divide and conquer algorithm with the incremental algorithm in comput-ing 3-D convex hulls. In 3-D cases, the incremental algorithm requires O(n log n) expected time (Clarkson and Shor, 1988; Edelsbrunner, 1987; Kallay, 1984; Mulmuley, 1994; Preparata and Shamos, 1985; Seidel, 1990). In each iterative routine of the incremental algorithm, the merged point is randomly selected so that the vertices of the convex hull can’t be found efficiently.Generally speaking, the Quickhull algorithm is evolved from the incremental algorithm. In construct-ing 2-D convex hulls, Eddy (1977) presented a no-tion to successively partition a set of planar points into several regions with binary trees. With the “throw-away” principle, Akl and Toussaint (1978) presented an algorithm in which the furthest outside point is selected for the selected edge of the current convex hull in each iterative routine and then the se-lected edge is replaced with two new edges. Instead of a triangle used by Eddy and a quadrilateral used by Akl (1978) and Bykat (1978) uses a line segment to divide planar points into two regions in the first step. For general-dimension Quickhull algorithms, Barber et al., (1996) proposed detailed procedures and empirical data. His algorithm is very efficient in con-structing general-dimension convex hulls.In this paper, a new Quickhull algorithm for building 3-D convex hulls is presented. We propose some efficient routines to find a tetrahedron as the initial convex hull and then build successively the new convex hull for each new selected vertex. In finding the boundary of all visible facets for a new selected vertex, a neighbor tree is used in this paper. Because Barber’s algorithm is one of the latest and efficient Quickhull algorithms, the efficiency of our algorithm is compared with that of Barber’s algorithm.II. METHODSIn some mathematical models, the vertex or facet enumeration is used for representing the convex hull. The vertex enumeration only contains all the vertices of the convex hull in random order. The facet enu-meration lists the inside halfspace for each facet of the convex hull. In this paper, each facet and its three neighboring facets of the current convex hull are recorded in a linked list. Compared with the data structures of previous Quickhull algorithms, a much simpler data structure is proposed in this paper to raise the efficiency of our algorithm. The procedure of our algorithm is described as follows and its pseudo-code is shown in Fig. 1 starting from the main routine CONVEX_HULL().(1)Record all the points of input point set in a linkedlist L s. Remove duplicated points from L s with anoctree. Substitute the coordinate of each point in L s into four formulas x +y + z, x - y - z, -x + y - z, and -x - y + z separately. Find out a point A in L s with the maximum value for the formula x + y + z and then take out point A from L s. Repeat the same process for points B, C, and D and remove them from L s one by one. Points B, C, and D have the maximum values for formulas x - y - z, -x + y - z, and -x - y + z respectively. Hence, points A, B, C, and D are definitely different. The initial tetrahe-dron is built with points A, B, C, and D if any three points of them are not collinear. The normal vec-tor of each facet of the initial tetrahedron must point outward. For each facet of the initial tetrahedron, its three neighboring facets are stored in a linked list. This part of the work has been done by the function FindInitialHull() in Fig. 1.(2)All the points in L s are partitioned into five setsby four facets of the initial tetrahedron in line (a) of Fig. 1. Four sets are outside the tetrahedron and the fifth set is inside the tetrahedron. For each facet T n, if there are points in front of T n, put T n in the tail of a linked list L p. Otherwise, put T n in the tail of another linked list L e. After these four facets have been put into L p or L e, connect L e af-ter L p forming a new linked list L h. Assume that the head of L h is the facet T j.(3)The work in line (b) of Fig. 1 is described asfollows. If the facet T j is NULL, the whole pro-cedure has been finished and all facets in L h form the final convex hull. If T j is inside the current convex hull, remove T j from the linked list L h, set the next facet in L h as T j, and then go back to step(3). If there is no point in front of T j, set the nextfacet in L h as T j and then go back to step (3). (4)Among all points in front of T j, find the point Pfurthest from T j. In line (c) of Fig. 1, set the facet T j as the root of a neighbor tree. Set three neigh-boring facets of T j as its three branches. Assume that the node T k is one of these three branches.(5)For the node T k, assume that the facet T a is theupper node of T k and T a, T b, and T c are three neigh-boring facets of T k in the neighbor tree. If T k is visible to point P, put T b and T c as two branches of T k into the neighbor tree in the same surround-ing order as T a, T b, and T c are around T k on the convex hull. If T k has already appeared in this neighbor tree, end the work of branch T k. If T k is not visible to point P, set T k as a boundary facetB n and end the work of branch T k. If there is anybranch T k whose work has not been ended, go back to step (5).(6)Search the neighbor tree and take out the ridgeshared by each boundary facet B n and the upper node facet of B n with the depth-first search. Con-nect each ridge with point P to form a facet forH. M. Chen and T. H. Lin: An Algorithm to Build Convex Hulls for 3-D Objects947 typedef struct {FACET neighboringFacet*[3], *nextFacet;bool isInsideFacet = False;int branchState[3]; /*record visible, repeated, or boundary for each neighboringFacet*/VERTEX *frontVertex; /*the furthest point stored in the head of this linked list*/} FACET;NeighborTree(FACET *currentNode, VERTEX *furthest, VERTEX *outsideVertex, FACET *facetList){currentNode->isInsideFacet = True;AddVertexToList(currentNode->frontVertex, outsideVertex); /*collect all points outside visible facets*/for (each branch FACET Tk of currentNode) {if (Tk has not appeared in the tree) {if (furthestVertex is in front of Tk)SetbranchState(visible); /*Tk is a visible facet*/elseSetbranchState(boundary); /*Tk is a boundary facet*/}elseSetbranchState(repeated); /*Tk is a repeated facet*/}for (each branch FACET Tj of currentNode)switch(branchState of Tj) {case “visible”: /*Tj is a visible facet*/NeighborTree(Tj, furthestVertex, outsideVertex, facetList);break;case “boundary”: /*Tj is a boundary facet*/newFacet = BuildOneFacet(); /*furthestVertex and two vertices shared by currentNode and Tj*/RecordNewNeighbor(); /*replace currentNode with newFacet as one neighboring facet of Tj*/AddToHead(newFacet, facetList);break;case “repeated”: /*Tj is a repeated facet*/break;default: break;}}PARTITION(VERTEX *vertexList, FACET *facetList, FACET *convexFacetList){for (each FACET Tn in facetList) {for (each VERTEX Pj left in vertexList)if (VERTEX Pj in front of FACET Tn)VertexAddToFacet(Pj, Tn); /*add Pj into the frontVertex of Tn*/if (Tn->frontVertex != NULL) /*some points are in front of Tn*/AddToList(Tn, convexFacetList);/*in convexFacetList, add Tn after the last facet that has outside points*/else /*no point is in front of Tn*/AddToListTail(Tn, convexFacetList); /*add Tn into the tail of convexFacetList*/}}CONVEX_HULL(VERTEX *vertexList){FACET *facetList, *convexFacetList = NULL;VERTEX *outsideVertex;facetList = FindInitialHull(vertexList); /*build the initial tetrahedron*/PARTITION(vertexList, facetList, convexFacetList); /*line (a)*/for (each FACET Tj in convexFacetList) { /*line (b)*/if (Tj->isInsideFacet) /*Tj is inside the convex hull*/DeleteFacet(Tj);else {if (Tj->frontVertex != NULL) {Tj->FindBoundary(Tj, frontVertex, outsideVertex, facetList); /*line (c)*/RecordNeighboringFacet(facetList); /*record neighboring facets for each new facet*/Rearrange(facetList); /*avoid two successive facets neighboring on convex hull*/PARTITION(outsideVertex, facetList, convexFacetList); /*line (d)*/Tj = convexFacetList; /*go back to the head of convexFacetList after each partitioning*/}}}}Fig. 1 The pseudo-code of our algorithm.948Journal of the Chinese Institute of Engineers, Vol. 29, No. 6 (2006)the new convex hull and put this facet into the tail of L h. Collect all points outside the facets of the new convex hull.(7) In line (d) of Fig. 1, partition all outside pointswith each new facet formed in step (6) using the same process as step (2). Set j = j + 1 and go to step (3).The procedures whole procedures of our algo-rithm whose starting point and terminal point are [Start] and [End] respectively is shown in Fig. 2.For 3-D cases mentioned above, four vertices A, B, C, and D are required to build the initial tetrahedron. In 2-D cases, only three points P1, P3, and P5 shown in Fig. 3 are needed to form the initial triangle. To demonstrate the whole procedure of our algorithm in a simpler way, a 2-D example is used. In order to describe one important process in our al-gorithm as shown in Fig. 3(b), the highest point in Fig. 3(a) is not chosen as one vertex, i.e., the point P1, for the initial triangle.In Fig. 3(a), all points are partitioned by facets in sequence of T1, T2, and T3. There are points in front of T2 and T3 but there is no point in front of T1.Facet T3 is after facet T2 in the partitioning sequence so T3 is put after T2 in the linked list of Fig. 4(a) and T1 is put in the tail of Fig. 4(a). Facet T2 is the first element with outside points in Fig. 3(a) so T2 is set as the root of the neighbor tree in Fig. 5(a). Among all points in front of T2 in Fig 3(a), find the furthest point P2 from T2. Facets T1 and T3 are the neighbor-ing facets of T2 and not visible to P2 so T1 and T3 are the boundary facets of this tree and set as the branches of the root in Fig. 5(a). The ridge shared by T1 and T2 is point P3 and the ridge shared by T2 and T3 is point P1. Connect P2 to P3 and P1 separately to get two new facets T4 and T5. All points which are in front of T2 are partitioned by T4 and T5 to get Fig. 3(b) and Fig. 4(b). Facet T2 becomes an inside facet in the current convex hull and is marked with a cross in Fig. 4(b) because T2 will not appear on the surface of the final convex hull.After T2 has been deleted in Fig. 3(b), T3 be-comes the first element with outside points in the linked list. Hence, set T3 as the root of the neighbor tree and T1 and T5 as two branches of T3 in Fig. 5(b). Among all points which are in front of T3, P4 is theAll facets in Lh form the final convex hull. [End]If there is any point in front of a facet Tn of the initial tetrahedron, put Tn in the tail of Lp; otherwise put Tn in the tail of Le. After four facets Tn are put into Lp or Le, connect Le after Lp to form Lh. The head of Lh is TjFind the ridge shared by each boundary facet Bn and Bn’s upper node facet. Connect each ridge with point P to form a facet of the new convex hull and put this facet into the tail of Lh. j = j + 1[Start] Findfour vertics for the initial tetrahdronIf there is any branch Tk whose work has notbeen endedyesnonoIf Tj is NULLIf Tj is inside thecurrent convex hullRemove Tj fromLh, j = j + 1If there are pointsin front of Tjj = j + 1yesyesnoAmong all points in front of Tj,find the furthest point P from Tj. Set Tj as the root of a neighbor tree and Tj’s three neighboringfacets Tk as Tj’s branchesTa, Tb, and Tc are threeneighboring facets of Tk andTa is the upper node of TkIf Tk is visible to point PSet Tb and Tc astwo branches of TkIf Tk has appeared inthe neighbor treeSet Tk as a boundary facetBn and end the work of TkEnd the work of TknonoyesyesyesnoFig. 2 The procedures of our algorithmH. M. Chen and T. H. Lin: An Algorithm to Build Convex Hulls for 3-D Objects 949furthest point from T 3 in Fig. 3(b). Facet T 1 is not visible to P 4 so T 1 is set as a boundary facet in Fig 5(b). Facet T 5 is visible to P 4 so T 5 is set as a visible facet. Aside from T 3, T 4 is another neighboring facet of T 5 and not visible to P 4 so T 4 is set as a boundary facet. Facets T 1 and T 4 are two boundary facets to P 4. The ridge between T 1 and its upper node, i.e., T 3,is P 5. Point P 2 is the ridge between T 4 and its uppernode, i.e., T 5. Connect P 4 to P 5 and P 2 to form T 6 and T 7 respectively. All points outside visible facets T 3and T 5 are partitioned by T 6 and T 7. Facets T 3 and T 5become inside facets in the current convex hull so they are marked with crosses in Fig 4(c). There are points outside T 6 and T 7 so T 6 and T 7 are inserted suc-cessively into the linked list after T 3 in Fig. 4(c).Points P 6 and P 7 are the furthest points from T 6and T 7 respectively in Fig. 3(c) and 3(d). After all inside facets in Fig. 3(e) have been deleted, all the facets of the final convex hull are composed of T 1,T 4, T 8, T 9, T 10, and T 11 as shown in Fig. 3(f) and 4(f).Only the vertices of the initial triangle or the furthest points can be the vertices of the final convex hull in 2-D examples.In Fig. 6(a) that is a 3-D example, light gray facets are visible and dark gray facets are not visible to the black point respectively. All visible facets and boundary facets are found with a neighbor tree. All ridges are located on the boundary between visible facets and invisible facets. Connect the black point to the two end points of each ridge to form a new facet. All visible facets will be inside the new con-vex hull so they will be deleted.In the 3-D example shown in Fig. 7(a), assume(a)P 2T 2T 3P 1T 1P 3(b)P 2P 5T 4T 5T 3P 4P 1T 1P 3(c)P 2P 6P 5P 2T 4T 6T 7T 1(d)P 6T 4T 7T 9T 8P 7T 1(e)P 7T 9T 4T 8T 10T 11T 1(f)T 4T 10T 11T 9T 8T 1Fig. 3A 2-D example and the processes of forming its final con-vex hullFig. 4 The linked lists for the 2-D example in Fig. 2Fig. 5 Four neighbor trees for the 2-D example in Fig. 2(a)(b)Fig. 6(a) Light gray facets are visible to the black point and dark gray facets are not visible to the black point. (b) Merge new facets into the old convex hull to form a new convex hull950Journal of the Chinese Institute of Engineers, Vol. 29, No. 6 (2006)that facet T 1 is set as the root of the neighbor tree in Fig. 7(b). Among all points that are in front of T 1,assume that P is the furthest point from T 1. On the convex hull, facets T 1 through T 6 are visible to P .Facets T 2, T 3, and T 4 are three neighboring facets of T 1 so set these three facets as the branches of T 1.Facets T 1, B 1, and B 2 are three neighboring fac-ets of T 2 and their surrounding order around T 2 in the neighbor tree of Fig. 7(b) must be accorded with that around T 2 on the convex hull of Fig. 7(a). Facet T 1 is the upper node of T 2 so set B 1, and B 2 as two branches of T 2. Facets B 1 and B 2 are not visible to P so they are boundary facets. Facets T 1, B 3, and T 5 are three neighboring facets of T 3 and T 1 is the upper node of T 3 so set B 3 and T 5 as two branches of T 3. In the similar way, B 4 and T 6 are set as two branches of T 5and B 5 and T 4 are set as two branches of T 6. Facet T 4has already appeared in the neighbor tree so T 4 is a repeated facet. Facets B 3, B 4, and B 5 are not visible to P so they are boundary facets. Other parts of the neighbor tree are built in the same way. The bound-ary of all visible facets is found when every leaf node in a neighbor tree is either a boundary facet or a re-peated facet.III. IMPLEMENTATION AND COMPARISONAssume that the plane equation of the facet A is f A (x , y , z ) = 0 and the coordinate of the point P is (x P ,y P , z P ). When building a neighbor tree in our algorithm,if f A (x P , y P , z P ) > –ε, facet A is defined as a visible facet to point P . When doing the partitioning pro-cess in our algorithm, if f A (x P , y P , z P ) > ε, P is de-fined as a point in front of facet A . In this paper, the value of ε is set to 16 times of the machine epsilon (2.22E-16). Under these two conditions, degenerate cases will not cause any vague situation in our algorithm.Models in Figs. 8(a) and 8(c) were created by the software. The model in Fig. 8(e) was made with clay and then scanned with the laser scanning system to get image data. Figs. 8(b), 8(d), and 8(f) are the convex hulls of models Figs. 8(a), 8(c), and 8(e)respectively. The last six cases in Table 1 were cre-ated by random distribution of points in a unit cube or on the surface of a unit sphere respectively.Our algorithm has been successfully implemented in C language with an Intel Pentium-4 1.6G personal computer. The source code of Barber’s algorithm is available via network address /download. In order to compare the net efficiency be-tween Barber’s algorithm and our algorithm, the timeFig. 7(a) A 3-D example. (b) The neighbor tree of the example in (a)Fig. 8Figures (a), (c), and (e) are three 3-D models. Figures (b), (d), and (f) are the convex hulls of models (a), (c),and (e) respectively(a)(b)(c)(d)(e)(f)H. M. Chen and T. H. Lin: An Algorithm to Build Convex Hulls for 3-D Objects951for reading data files is subtracted from the whole running time. Each datum in Table 1 is the average time for running the corresponding algorithm 30 times on the corresponding model.For storing facets, double linked lists are used in Barber’s algorithm, but single linked lists are used in our algorithm. As a visible facet is deleted from the double linked list in Barber’s algorithm, the pre-vious element and the next element of the deleted facet will be connected. Hence, any element in the double linked list must have two pointers to the pre-vious element and the next element separately. In our algorithm, visible facets are found and marked in traversing the neighbor tree, and deleted in the next traverse of the linked list. Hence, the time for double linked lists is longer than that for linked lists in do-ing the similar work. This is the first point where our algorithm is better than Barber’s algorithm.In Barber’s algorithm, the memory cell for each ridge is allocated first and then two neighboring facets and two endpoints are stored into this cell. Ridges found by Barber on the outer boundary of all visible facets are randomly stored and then these ridges form new facets with the furthest point. All new facets must be searched with a hash table to find neighboring rela-tions among them. This extra work is not necessary in our algorithm because the neighboring sequence of ridges appears in the neighbor tree. This is the second point where our algorithm is better than Barber’s algorithm.All outer points to visible facets must be parti-tioned by new facets which are formed with the outer boundary of these visible facets. In Barber’s algorithm, any two successively selected partitioning facets may be neighboring on the new convex hull. In our algorithm, two successively selected partitioning facets are arranged to avoid being neighboring facets on the new convex hull. Therefore, the total number of op-erations of substituting an outer point into the plane equation of a partitioning facet in our algorithm is less than that in Barber’s algorithm. This is the third point where our algorithm is better than Barber’s algorithm.The time complexity of our algorithm is O(n log r), where n is the number of input points and r is the number of processed points. Although the time com-plexity order of our algorithm is the same as that of Barber’s algorithm, our algorithm is more efficient than Barber’s algorithm due to above three points in qualitative comparisons. In quantitative comparisons, the efficiency of our algorithm is over twice that of Barber’s algorithm for those nine models in Table 1.IV. CONCLUSIONSIn this paper, the neighbor tree is proposed to find visible facets and ridges on the outer boundary of these visible facets. The data structure of our al-gorithm is simpler than that of Barber’s algorithm. New facets found in our algorithm appear in neigh-boring sequence but these new facets must be arranged again in an extra process in Barber’s algorithm. The order of partitioning facets to partition outer points in our algorithm is more efficient than that in Barber’s algorithm. In both qualitative and quantitative comparisons, our algorithm is more efficient than Barber’s algorithm.ACKNOWLEDGMENTSWe gratefully acknowledge the support of the National Science Council of the Republic of China for this research under the grant NSC 93-2212-E-002-061, and specially thank Ms. Yue-Jun Chen for mak-ing the clay model of Fig. 8(e) and Mr. Ming-Hui Lin for getting the image data of this model with the la-ser scanning system.Table 1 The efficiency comparison between Barber’s algorithm and our algorithm on nine modelsNumber ofNumber of Barber’s OurNumber of point on Efficiency Models faces on the algorithm algorithmpoints the convex ratioconvex hull(ms)(ms)hullFig. 8(a)131,32931,87163,7381,425498 2.86 Fig. 8(c)288,00025,86751,7302,140793 2.70 Fig. 8(e)634,7123,4976,9901,320541 2.4430,0001713385424 2.25 Points in a300,000240476550216 2.55 cube3,000,0003727406,2653,120 2.0110,00010,00019,996272114 2.39 Points on a100,000100,000199,9962,9711,306 2.27 sphere1,000,0001,000,0001,999,99645,53018,215 2.50952Journal of the Chinese Institute of Engineers, Vol. 29, No. 6 (2006)REFERENCESAkl, S. G., and Toussaint, G. T., 1978, “A Fast Con-vex Hull Algorithm,” Information Processing Letters, Vol. 7, No. 5, pp. 219-222.Allison, D. C. S., and Noga, M. T., 1997, “Comput-ing the Three-Dimensional Convex Hull,” Com-puter Physics Communications, Vol. 103, No. 1, pp. 74-82.Anderson, K. R., 1978, “A Reevaluation of an Effi-cient Algorithm for Determining the Convex Hull of a Finite Planar Set,” Information Processing Letters, Vol. 7, No. 1, pp. 53-55.Atwah, M. M., Baker, J. W., and Akl, S. G., 1995,“An Associative Implementation of Graham’s Convex Hull Algorithm,” Proceedings of the Sev-enth IASTED International Conference on Par-allel and Distributed Computing and Systems, Washington D.C., USA, pp. 273-276.Atwah, M. M., Baker, J. W., and Akl, S. G., 1996,“An Associative Implementation of Classical Convex Hull Algorithms,” Proceedings of Eighth IASTED International Conference on Parallel and Distributed Computing and Systems, Chicago, IL, USA, pp. 435-438.Atwah, M. M., and Baker, J. W., 2002, “An Associa-tive Static and Dynamic Convex Hull Algorithm,”Proceedings of the International Parallel and Dis-tributed Processing Symposium, Fort Lauderdale, FL, USA, pp. 15-19.Barber, C. B., Dobkin, D. P., and Huhdanpaa, H., 1996, “The Quickhull Algorithm for Convex Hulls,” ACM Transactions on Mathematical Software, Vol. 22, No. 4, pp. 469-483.Bykat, A., 1978, “Convex Hull of a Finite Set of Points in Two Dimensions,” Information Process-ing Letters, Vol. 7, No. 6, pp. 296-298. Chand, D. R., and Kapur, S. S., 1970, “An Algorithm for Convex Polytopes,” Journal of the Association for Computing Machinery, Vol. 17, No. 1, pp. 78-86. Clarkson, K. L., and Shor, P. W., 1988, “Algorithms for Diametral Pairs and Convex Hulls That Are Optimal, Randomized and Incremental,” Proceed-ings of the Fourth Annual ACM Symposium on Computational Geometry, Urbana-Champaign, IL, USA, pp. 12-17.Day, A. M., 1990, “The Implementation of An Algorithm to Find The Convex Hull of a Set of Three-dimensional Points,” ACM Transactions on Graphics, Vol. 9, No. 1, pp. 105-132.Eddy, W. F., 1977, “A New Convex Hull Algorithm for Planar Sets,” ACM Transactions on Math-ematical Software, Vol. 3, No. 4, pp. 398-403. Edelsbrunner, H., 1987, Algorithms in Combinatorial Geometry, Springer-Verlag, Heidelberg, Germany, pp. 139-176.Graham, R. L., 1972, “An Efficient Algorithm for Determining the Convex Hull of A Finite Planar Set,” Information Processing Letters, Vol. 1, No.4, pp. 132-133.Jarvis, R. A., 1973, “On the Identification of The Convex Hull of a Finite Set of Points in The Plane,” Infor-mation Processing Letters, Vol. 2, No. 1, pp. 18-21.Kaasalainen, M., and Torppa, J., 2001, “Optimization Methods for Asteroid Lightcurve Inversion,”ICARUS International Journal of Solar System Studies, Vol. 153, No. 1, pp. 24-36.Kallay, M., 1984, “The Complexity of Incremental Convex Hull Algorithms in R d,” Information Pro-cessing Letters, Vol. 19, pp. 197.Koplowitz, J., and Jouppi, D., 1978, “A More Effi-cient Convex Hull Algorithm,” Information Processing Letters, Vol. 7, No. 1, pp. 56-57. Mulmuley, K., 1994, Computational Geometry: An Introduction Through Randomized Algorithms, Prentice-Hall, Englewood Cliffs, NJ, USA, pp.96-105.O’Rourke, J., 1993, Computational Geometry in C, Cambridge University Press, New York, USA, pp.113-167.Preparata, F. P., and Hong, S. J., 1977, “Convex Hull of A Finite Set of Points in Two and Three Dimensions,” Communications of the ACM, Vol.20, No. 2, pp. 87-93.Preparata, F. P., and Shamos, M. I., 1985, Computa-tional Geometry: An Introduction, Springer-Verlay, New York, USA, pp. 95-145.Robert, L., and Faugeras, O. D., 1995, “Relative 3D Positioning and 3D Convex Hull Computation fromA Weakly Calibrated Stereo Pair,” Image andVision Computing, Vol. 13, No. 3, pp. 189-196. Seidel, R., 1990, “Linear Programming and Convex Hulls Made Easy,” Proceedings of the Sixth An-nual ACM Symposium on Computational Geometry, Berkeley, CA, USA, pp. 211-215.Sherali, H. D., Smith, J. C., and Selim, S. Z., 2001,“Convex Hull Representations of Models for Com-puting Collisions Between Multiple Bodies,”European Journal of Operational Research, Vol.135, No. 3, pp. 514-526.Sugihara, K., 1994, “Robust Gift Wrapping for The Three-dimensional Convex Hull,” Journal of Computer and System Sciences, Vol. 49, No. 2, pp. 391-407.Sugihara, K., 2000, “Three-Dimensional Convex Hull As a Fruitful Source of Diagrams,” Theoretical Computer Science, Vol. 235, No. 2, pp. 325-337.Manuscript Received:Jul.08,2005Revision Received:Dec.15,2005and Accepted:Feb.07,2006。

route distinguisher格式-概述说明以及解释1.引言1.1 概述概述在现代网络通信中，路由器扮演着至关重要的角色，负责将数据包从源地址传送到目标地址。

在大型网络中，不同的路由器需要能够识别和区分彼此所传输的数据包，并进行正确的路由选择。

为了解决这一问题，引入了route distinguisher（路由区分器）的概念。

route distinguisher是一种在虚拟专用网（VPN）中使用的标识符，用于唯一标识不同的路由器或VPN实例。

通过使用route distinguisher，可以确保在网络中的不同路由器或VPN实例之间进行正确的路由选择，避免数据包传输错误路由或丢失的情况发生。

本文将重点介绍route distinguisher的概念、作用以及格式，并探讨其在网络中的重要性和应用前景。

通过深入了解route distinguisher，读者将能更好地理解和应用该技术在实际网络中的作用。

1.2 文章结构本文主要分为三个部分，分别是引言、正文和结论。

在引言部分中，我们将对route distinguisher进行概述，介绍文章的结构和目的，为读者提供一个全面的背景了解。

在正文部分，我们将详细讨论什么是route distinguisher，以及它在网络中的作用和重要性。

同时，我们还将介绍route distinguisher的格式，帮助读者更好地理解这一概念。

最后，在结论部分，我们将总结route distinguisher的重要性，并展望它未来在网络中的发展和应用前景。

希望通过本文的阐述，读者能更深入地了解和应用route distinguisher。

1.3 目的route distinguisher是在虚拟专用网络(VPN)中用来唯一标识不同的路由信息的一个重要组件。

其目的主要是为了解决在多个VPN网络中可能出现的路由信息重叠和冲突的问题。

通过引入route distinguisher，可以确保在不同的VPN网络中的路由信息能够被正确识别和区分，从而保证网络的稳定性和可靠性。

Cooper Industries Inc.Crouse-Hinds DivisionIF 1540PO Box 4999, Syracuse, New York 13221 • U.S.A.Revised 11/08Copyright© 2007, Cooper Industries, Inc.Page 1Installation Instructions for UX EXIT Series - HAZLED, Self-Powered, Self-Diagnostic Battery BackupIF 1540WARNINGTo avoid electrical shock:WARNINGWARNINGWALL MOUNT -Exit StencilPry NotchShieldSnap-Out Chevrons(2) Screws (Supplied By Others)Frame/Mounting BaseBack GasketFigure 2Hub- 1/2 NPT conduit Sealing GasketKnockout at desired location Conduit bushed nippleThis fixture is provided with maximum of three sets of knockouts for alternate mounting orientation. There are three alternative mounting orientations:●Wall mount ●Ceiling mount ●End mountJunction box is used for mounting only. All wires must be routed through e standard wire 18 - 16 AWG or Solid wire 18 - 17 AWGTo mount on a wall:(see Figure 2)1. Remove exit stencil assembly from frame by prying up on the notches along the edge.2. Remove knockout for CONDUIT HUB at the desired location, with hammer and screwdriver, or drill out with 7/8” diameter hole saw.3. Knock out the appropriate mounting pattern on the MOUNTING BASE for the J-box being used. Also, the (2) 3/8” diameter mounting holes are to be utilized for installation and proper seal of the BACK GASKET. Remove backing from gasket during gasket installation.4. Install conduit hub and sealing gasket that comes with the fixture. See Figure 15. Complete the conduit installation with approved 1/2” CONDUIT and e 1/2” liquid tight fittings for sealing against moisture.6. Connect power supply in accordance with Local Codes and the NEC Code for Class I, Div. 2 Hazardous Location. All wires must be routed through conduit.Cooper Industries Inc.IF 1540Crouse-Hinds DivisionRevised 11/08PO Box 4999, Syracuse, New York 13221 • U.S.A.Page 2Copyright© 2007, Cooper Industries, Inc.To mount on a ceiling or end mount:(see Figure 3 & 4)1. Remove exit stencil assembly from frame by prying up on the notches along the edge (See Figure 1)2. Knockout: Remove knockout with hammer and screwdriver, or drill out with 7/8” hole saw.a. For Canopy: Ceiling mounting : remove Top knockout as shown in Figure 3. End mounting : remove knockout on left or right of the fixture as shown in Figure 4.b. Conduit Hub: Ceiling mounting : remove left or right knockout as desires Figure 3. End mounting remove top or unused side knockout as desired Figure 4.3. Remove the inner GASKET for use with the CANOPY and the JUNCTION BOX BRACKET. Remove backing from gasket. Attach the GASKET and mount the BRACKET and CANOPY to the J-box with (4) screws. Mount the FRAME securely to the CANOPY with (2) screws 1/4” - 20 UNC x 1” long and WASHER.4. Install conduit hub and sealing gasket that comes with the fixture. (see Figure 1)5. Complete the conduit installation with approved 1/2” CONDUIT and FITTINGS. Use 1/2” liquid tight fittings for sealing against moisture.6. Connect power supply in accordance with Local Codes and the NEC Code for Class I, Div. 2 Hazardous Location. All wires must be routed through conduit.Wire connections as follows: 120V line to black lead, neutral to white lead. Cap unused wires.1. Insert the wires into appropriate PUSH IN connector located on the TRANSFORMER in the EXIT STENCIL .2. Route the wires neatly around the EXIT STENCIL wire retaining clips. Push and snap-in the EXIT STENCIL into the FRAME . Check installation by checking the EXIT STENCIL ensuring that it is flush mounted onto the FRAME and that the wires are routed properly around the EXIT STENCIL . 3. Check the “O” RING in the FRAME , ensuring it is clean from dirt. Mount the SHIELD onto the FRAME . With the SCREWS and “O” RINGS provided, check to see that one “O” RING is under the SCREW HEAD and one “O” RING is holding the screw inside of the SHIELD . Tighten the SCREWS on the SHIELD securely, do not over tighten. Push down on the sheild to ensure the are sealed properly against the FRAME “O” RING .4. Energize the AC supply, LED display will illuminate.CEILING MOUNTGasketBracket Canopy"O" Ring Screw(2) Screws - Washes 1/4"-20UNC x 1"LGGreen Ground Screw7/8 Dia. Knockouts on inside top, left & right side locations.Figure 3(2) Screws Supplied By Others(2) Screws - Washes 1/4"-20UNC x 1" LGGreen Ground ScrewGasketGasketEND MOUNTFigure 4GasketCanopyBracketCooper Industries Inc.IF 1540Crouse-Hinds DivisionRevised 11/08PO Box 4999, Syracuse, New York 13221 • U.S.A.Page 2Copyright© 2007, Cooper Industries, Inc.Risque d’incendie/de choc electrique. Contacter Risk of Fire/Electric shock. If not qualified,TO PREVENT FIRE OR EXPLOSION。

ISP级软件路由器之王RouerOS 宽带接入服务器用户手册――配置指南RouerOS 系列宽带接入服务器配置指南内容摘要一．概述 (3)1．RouerOS 宽带接入服务器的网络接口类型 (3)2．RouerOS 宽带接入服务器具有以下网络功能 (3)二．基本的配置管理 (5)1 1．系统的缺省帐号 (5)1 2．登录方式 (5)1 3．命令行配置的基本操作 (6)1 远程管理-权限管理 (7)1 5．日志管理 (8)1 91 7．系统时间设置 (10)8. 系统热启动 (10)三．物理接口的配置管理 (10)四．查看当前配置 (11)4.1 查看全部配置 (11)4.2 查看子项配置 (11)五．IP 参数配置 (11)1 1. 路径： (11)1 2. 功能： (11)1 3. 配置IP 地址及路由 (12)1 4. 配置Firewall (14)1 5. 配置IP Service，限定远程管理RouerOS 的地址和方式 (16)1 6. 配置Hotspot（WEB 认证） (16)1 7. 配置IP Pool (16)1 8. 启用NAT 后的策略路由配置 (16)六．配置ppp 参数 (21)1. 配置PPP 模板 (22)2. 配置Radius-client (22)七．PPPoE 配置 (23)八．HOTSPOT 配置 (25)九．VLAN 配置 (30)十．VPN 配置 (31)10.1 PPTP VPN (31)10.2 EOIP VPN (32)十一．DHCP 配置 (33)11.1 DHCP Server (33)MAC 地址(及IP 地址)与端口绑定 (34)十二．防火墙配置 (35)12.1 防“冲击波”病毒 (35)十三. 配置文件的备份与恢复 (36)1 1. 显示文件系统 (36)1 2. 备份配置文件 (36)1 3. 恢复配置文件 (37)1 4. 配置文件上载与下载 (37)1 5. 配置复位 (37)1 6. 查看系统资源状况 (37)2 7. 监视端口流量 (37)Reference： (37)一．概述RouerOS 宽带接入服务器是基于嵌入式专用网络操作系统而设计的，具有丰富的网络接口，具备多数常见的网络设备功能，处理能力超群，运行十分稳健，性价比极高。

ros7 创建路由规则ROS7是一种流行的开源机器人操作系统，它提供了强大的功能和灵活性，可以帮助用户创建复杂的路由规则。

在本文中，我将介绍如何使用ROS7来创建有效的路由规则，并解释它们的作用。

让我们来了解一下什么是路由规则。

路由规则是一个决定数据包如何从源地址传输到目标地址的规则集合。

它可以帮助网络管理员管理和控制网络流量，确保数据包能够按照预期的方式传输。

在ROS7中，创建路由规则非常简单。

您只需要使用一些基本的命令和参数就可以完成。

下面是一个示例：```/ip routeadd dst-address=192.168.0.0/24 gateway=192.168.1.1```在这个示例中，我们创建了一条路由规则，将目标地址为192.168.0.0/24的数据包发送到网关为192.168.1.1的设备。

这意味着所有目标地址为192.168.0.0/24的数据包都将通过该网关进行传输。

除了基本的路由规则，ROS7还支持更高级的路由功能，如负载均衡和路由过滤。

您可以使用不同的命令和参数来配置这些功能，以满足您的特定需求。

例如，如果您想实现负载均衡，可以使用以下命令：```/ip routeadd dst-address=192.168.0.0/24 gateway=192.168.1.1,192.168.1.2 ```在这个示例中，我们将目标地址为192.168.0.0/24的数据包同时发送到网关192.168.1.1和192.168.1.2，以实现负载均衡。

这样可以有效地分担网络流量，提高网络的吞吐量和性能。

ROS7还支持路由过滤，您可以使用以下命令来配置路由过滤：```/ip routeadd dst-address=192.168.0.0/24 gateway=192.168.1.1 check-gateway=ping```在这个示例中，我们配置了一条路由规则，只有在网关192.168.1.1可达时才发送目标地址为192.168.0.0/24的数据包。