A coarse-grained multicomputer algorithm for the longest common subsequence problem
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刊名简称刊名全称ISSN小类名称(中文)0269-9648工程:工业PROBABILITY IN THE ENGINEERING AND INFORPROBAB ENG INFORAPPL MATH MODEL A PPLIED MATHEMATICAL MODELLING0307-904X工程:综合0927-6467工程:综合RUSS J NUMER ANARUSSIAN JOURNAL OF NUMERICAL ANALYSIS AN1239-6095环境科学ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MBOREAL ENVIRON R0167-9473计算机:跨学科应用COMPUT STAT DATACOMPUTATIONAL STATISTICS & DATA ANALYSISJ COMB OPTIM JOURNAL OF COMBINATORIAL OPTIMIZATION1382-6905计算机:跨学科应用0094-9655计算机:跨学科应用J STAT COMPUT SIJOURNAL OF STATISTICAL COMPUTATION AND S1387-3954计算机:跨学科应用MATH COMP MODELMATHEMATICAL AND COMPUTER MODELLING OF DMATHEMATICAL AND COMPUTER MODELLING0895-7177计算机:跨学科应用MATH COMPUT MODEMATHEMATICS AND COMPUTERS IN SIMULATION0378-4754计算机:跨学科应用MATH COMPUT SIMUQUEUEING SYST QUEUEING SYSTEMS0257-0130计算机:跨学科应用1615-3375计算机:理论方法FOUNDATIONS OF COMPUTATIONAL MATHEMATICSFOUND COMPUT MATFUZZY SET SYSTFUZZY SETS AND SYSTEMS0165-0114计算机:理论方法COMPUT COMPLEXCOMPUTATIONAL COMPLEXITY1016-3328计算机:理论方法STAT COMPUT STATISTICS AND 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zoj(zju)题目分类(ZOJ (ZJU) topic classification)DP:1011柱简单题1013大设备简单题1024游戏简单题日历1027人类基因的功能简单题1037简单题格里德兰1052阿尔杰农的有害排放简单题1409通信系统简单题,但是很容易看错~ ~ ~1425交叉匹配简单题1438颗小行星!简单题1459弦的距离和变换过程简单题1462把他们分组!简单题1556英雄无敌简单题,不过背景蛮有意思的......1520免税店简单题1524超市简单题1301新的别墅简单题1303陪审团的妥协其实不是很难,但是很容易错,555 ......1345最好的交易简单题,但是也很容易错...... 555 ......1360雷达安装简单题1396个问题:2054简单题伞1058货币兑换简单题1076基因组合简单题1092套利简单题1093只猴子和香蕉简单题1094矩阵链相乘简单题1536个迷宫简单题1100蒙德里安的梦想简单题,DP可以过,不过据说有复杂的组合公式图简单题上涨11031134战略游戏简单题1147格式化文本简单题1148游戏简单题1161去钓鱼简单题1180自数简单题1192这是不是一个错误,这是一个特征!简单题1196快餐简单题1107字母和奶酪简单题,不过题目描述有些混乱1136多简单题,BFS1276优化阵列乘法序列简单题1255路简单题1250总是在奔跑简单题1213木材切削简单题1206赢得奖金简单题1479无聊题Dweep1587 100无聊题,DP应该可以......但是太烦了......没做......1066方冰无聊题,目前已知的O(nlogn)算法要用AVL ......您有没有简单点的O(nlogn)的算法?1245个三角形无聊题1022个平行的期望经典题,想了N久,最后发现可以DP,相当好的一道题1499增加序列经典题{ }1039数字游戏没有完美解决的题,感觉可以直接以所有剩下的数作为状态DP,但是缺乏证明......1227免费的糖果srbga的经典题,我看了oibh上的解题报告才做出来的......:(1234筷子srbga的经典题......图论:1525防空简单题,Minimum path coverage1500 Pre-Post-erous! Simple question!1501, Knockout, Tournament, simple questions1508 Intervals should be a simple question for you, but I've been thinking about n for a long time...... Differential system1333, Galactic, Import, simple questions1304 Tin Cutter simple question, but there seems to be a spacecomplexity of O (n) algorithm1310 Robot simple questions1311 Network simple questions1344, A, Mazing, Problem, simple questions1395, Door, Man, simple questions, Euler loops1372 Networking simple questions1406, Jungle, Roads, simple questions1053, FDNY, to, the, Rescue! Simple question1055, Oh, Those, Achin, Feet, a good simple question1059, What, s, In, a, Name, simple questions1064, Roads, Scholar, simple questions1082, Stockbroker, Grapevine, simple questions1085 Alien Security simple question, I think my algorithm was so clever:)1097, Code, the, Tree, simple questions1060 Sorting It All Out simple question, but if the scale is larger......1105, FatMouse, s, Tour, simple questions1119 SPF simple questions1127, Roman, Forts, simple questions1140 Courses simple questions1157, A, Plug, for, UNIX, quite a simple question1203 Swordfish simple questions1221, Risk simple questions, the shortest path1197, Sorting, Slides, simple questions, matching1268, Is, It, A, Tree? Good question, graph theory1273, It, s, Ir-Resist-Able, simple questions, graph theory1298 Domino Effect simple question, the longest way1260 King simple problem, differential restriction system......1291 MPI Maelstrom, a good question, the longest way1266 Gossiping simple questions1285 Shipping Routes boring questions, the shortest line1313, Gears, on, a, Board, boring questions1502 Plugged In boring questions, matching should be OK, but too boring, did not do......1568 WishingBone s Room Plan boring questions, the maximum and minimum matching error, but easy to see.1077 Genetic Combinations boring questions, matching1364 Machine Schedule recitation questions...... Matching......1137, Girls, and, Boys, reciting questions, matching......1023 University Entrace Examination classic questions, but repeat with 15761576, Marriage, is, Stable classic questions, touching background, classic algorithms......1249, Pushing Boxes classic question, someone's paper written, cut point and block +BFS can be done in O (area) time, but this question seems to have been relatively old1141, Closest, Common, Ancestors, without the perfect solution, the simplest algorithm can be passed, but if the scale is large......1084, Channel Allocation hasn't been solved perfectly. I'vesearched for it, but do you have a better algorithm?1231 Mysterious Mountain SRbGa classic questions......1232, Adventure, of, Super, Mario, SRbGa classic questions......Mathematics:1007个数值求和一系列简单题,还是蛮有意思的1045简单题宿醉1049我想我需要一个游艇简单题1028翻转和移位简单题,可以DP /石/ ......,但是实际上有数学方法可以直接判断出来1026模块化多项式乘法简单题,感觉有比较简单的好算法,但想不出来:(1307包简单题,不过也蛮经典的......1312总理削减简单题1334从根本上说简单题1337 PI简单题1342字索引简单题1349四季度简单题1350简单题醉卒1352进制数的转换简单题1353规模不大单峰回文分解,所以是简单题......1354扩展熄灯简单题1362游戏的预测简单题1365里程银行简单题1382一个简单的任务简单题1383二进制数简单题1403简单题窃贼1408有趣的数字系统简单题1486彩色树简单题1487张扑克牌简单题1489 2 ^ x mod n = 1简单题,应该有好算法,不过枚举就可以过...... 1503一个人“价格是正确的”简单题,POI鸡蛋的翻版1512水处理厂简单题,组合计数1526大数简单题,不过O(1)和O(n)还是有区别的:)1529神秘的旅行简单题,不过个人感觉题目描述很令人费解1530找到多个简单题1537玩计算器简单题1577最大公约数和LCM简单题,分区联赛的题...... 1005壶简单题1543简单题stripies1569部分和简单题为了简单题1062树1070简单题Bode图1073我们绕圈走简单题,142857,我喜欢^ _ ^1078简单题回文数字1086部分简单题八进制交叉简单题1199点1104次飞跃高楼简单题1110迪克和简简单题1115个数字的根简单题1113你计算E简单题1152数学的好奇心简单题1154,数字简单题1160生物节律简单题1163楼梯简单题1177号简单题k-魔术1184美元假钞简单题1182保持向前…简单题,我喜欢:)1284完善简单题1272讲简单题数值1269椰子,重新简单题1247到处都是宝藏!简单题1241几何作了简单的简单题1202分算简单题1216甲板简单题1218比简单题1261优质土地简单题1212山地景观无聊题1410号序列无聊题1401希尔伯特曲线的交叉点无聊题1331完美的立方体无聊题1322随机数无聊题1535幸运票无聊题1539很多无聊题1363巧克力经典题......1366经典题强烈推荐提款机!1149分经典题,应该可以用1366的方法做,但似乎可以利用问题的特殊性用贪心+ DP在O(1)的时间内做出来1222只是事实经典题,没有完美解决我的做法是O(logN ^,2)的,据说可能有O(logN)的做法,但我没想到:(1475 ranklist没有完美解决,不知道您有没有好方法......1572手镯~ ~ ~题义不明,感觉可能是判定欧拉回路的存在性,但是过不去,555 ......1133史密斯数没有完美解决,数学1080直接减尚未解决,我过的程序是错的,想和您讨论~ ~ ~ 1229礼物吗?srbga的经典题......!1238猜数srbga的经典题......1239河内塔麻烦再次!srbga的经典题......字符串处理:1050启动启动简单题1315个借口!简单题1151字的反转简单题,好像是什么实践的......1170字符串匹配简单题1174字母代码不错的简单题跳过1175文字处理机简单题1181字的融合简单题1038 T9无聊题,单词树1330 DNA翻译无聊题1335个字母的序列分析无聊题1099 HTML无聊题1243网址无聊题1540审查!强烈推荐经典题!1511字谜没有完美解决的题,可以用后缀树......但是没多大意义......而且我通过的程序是错的......搜索:1002消防网简单题,ceoi2002的警卫的缩小版,搜索就可以1003简单题崩溃气球,很微弱的的题目,想了半天,最后发现最简单的搜索就能过1004个字谜的堆栈简单题,同样微弱1320简单题DEL命令1496最适合简单题1179发现矩形简单题1190优化程序简单题1217八简单题1204简单题添加剂方程1219个比萨饼吗?简单题1036谜2无聊题,终于耐心读完题目后发现是简单的搜索+模拟......微弱的......建议不要看......1089大乐透无聊题1054保时捷无聊题1302艘......题1031平方的驱逐舰变态题,:(:(:(:(,狂剪枝才过的......1297角变态题,标准解法是搜索......1008侏儒数字魔方经典题,个人感觉是很不错的卡时搜索,不过似乎IOI不会出这种题型......1380经典题强烈推荐片!1252岛的逻辑经典题,不过也够老了......1237粉丝和宝石srbga的经典题,变态,但是很有趣:)模拟:1051行业新的增长简单题1300个边境简单题1326 M*A*S*H简单题1494简单题爬1072单片机模拟简单题1098简单的计算机简单题1056简单题蜗杆转动1195简单题熔丝熔断1189数字计数简单题1144抢劫简单题1153比赛直播简单题,但是直接计算好像不行,得模拟......:(1167棵树在水平简单题1200挖掘简单题1278伪随机数简单题1257停车场简单题1270个旅行简单题1207骑士,公主与龙无聊题1169方密码无聊题1176模具和棋盘无聊题1178本小册子印刷无聊题1009谜无聊题,但是很容易错......:(1012主机无聊题,但是很容易错......:(1324无聊题UNIX LS,输出格式没说清楚~~~~~~~ 1336标记无聊题1277可转让投票无聊题1279 cowculations无聊题1281该无聊题1282呼叫转移无聊题1065机器人变态题,太复杂啦~~~~~~~~~~~1208辊模!变态题1388经典题强烈推荐交流!1236吃还是不吃?srbga的经典题......模拟几何:1575科赫曲线简单题1010区简单题1565输入简单题1081点在简单题1165激光线简单题,但是算法能否再改进呢......?1248视频监控简单题,李彭煦的论文中写到过,好像是某年CTSC 的......1299摆简单题,我蛮喜欢的:)1090圆的周长无聊题1271在Windows无聊题1280相贯线无聊题1296星经典变态题......1030的耕地变态题......现在我都为自己当时居然能做出来感到不可思议......1041变送器变态题......好烦人......现在绝对没有信心再做一遍了......1158寻宝之经典题,教会我的......1139矩形没有完美解决其它:1006做解开简单题1014操作数简单题1016 parencodings简单题1042 W的密码简单题1047图像的周长简单题1514假票简单题1029简单题运动表,好像是线段树的经典题目之一,但是这题规模比较小,所以不必用。
关于序列二次规划(SQP)算法求解非线性规划问题研究兰州大学硕士学位论文关于序列二次规划(SQP)算法求解非线性规划问题的研究姓名:石国春申请学位级别:硕士专业:数学、运筹学与控制论指导教师:王海明20090602兰州大学2009届硕士学位论文摘要非线性约束优化问题是最一般形式的非线性规划NLP问题,近年来,人们通过对它的研究,提出了解决此类问题的许多方法,如罚函数法,可行方向法,Quadratic及序列二次规划SequentialProgramming简写为SOP方法。
本文主要研究用序列二次规划SOP算法求解不等式约束的非线性规划问题。
SOP算法求解非线性约束优化问题主要通过求解一系列二次规划子问题来实现。
本文基于对大规模约束优化问题的讨论,研究了积极约束集上的SOP 算法。
我们在约束优化问题的s一积极约束集上构造一个二次规划子问题,通过对该二次规划子问题求解,获得一个搜索方向。
利用一般的价值罚函数进行线搜索,得到改进的迭代点。
本文证明了这个算法在一定的条件下是全局收敛的。
关键字:非线性规划,序列二次规划,积极约束集Hl兰州人学2009届硕二t学位论文AbstractNonlinearconstrainedarethemostinoptimizationproblemsgenericsubjectsmathematicalnewmethodsareachievedtosolveprogramming.Recently,Manyasdirectionit,suchfunction,feasiblemethod,sequentialquadraticpenaltyprogramming??forconstrainedInthisthemethodspaper,westudysolvinginequalityabyprogrammingalgorithm.optimizationproblemssequentialquadraticmethodaofSQPgeneratesquadraticprogrammingQPsequencemotivationforthisworkisfromtheofsubproblems.OuroriginatedapplicationsinanactivesetSQPandSQPsolvinglarge-scaleproblems.wepresentstudyforconstrainedestablishontheQPalgorithminequalityoptimization.wesubproblemsactivesetofthesearchdirectionisachievedQPoriginalproblem.AbysolvingandExactfunctionsaslinesearchfunctionsubproblems.wepresentgeneralpenaltyunderobtainabetteriterate.theofourisestablishedglobalconvergencealgorithmsuitableconditions.Keywords:nonlinearprogramming,sequentialquadraticprogrammingalgorithm,activesetlv兰州大学2009届硕士学位论文原创性声明本人郑重声明:本人所呈交的学位论文,是在导师的指导下独立进行研究所取得的成果。
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ACoarse-GrainedMulticomputerAlgorithmfortheLongestRepeatedSuffixEndingatEachPointinaWord
ThierryGarciaandDavidSem´eLaRIA:LaboratoiredeRechercheenInformatiqued’AmiensUniversit´edePicardieJulesVerne,CURI,5,rueduMoulinNeuf,80000Amiens,France{garcia,seme}@laria.u-picardie.fr
Abstract.ThepaperpresentsaCoarse-GrainedMulticomputeralgo-rithmthatsolvestheproblemoffindingthelongestrepeatedsuffixend-ingateachpointinaword.ThisalgorithmcanbeimplementedintheCGMwithPprocessorsinO(N22ThierryGarciaandDavidSem´esuitedforadesignofalgorithmsthatarenottoodependentonanindividualarchitecture.Wesummarizetheassumptionsofthismodel:•allalgorithmsperforminso-calledsupersteps,thatconsistofonephaseofinterprocessorcommunicationandonephaseoflocalcomputation,•allprocessorshavethesamesizeM=O(N
s(P),whereTistheruntimeofthebestsequentialalgorithmonthesamedataands(P),thespeedup,isafunctionthatshouldbeasclosetoPaspossible.Tobeabletodoso,itisconsideredasagoodideathefactofkeepingthenumberofsuperstepsofsuchanalgorithmaslowaspossible,preferablyO(M).AsalegacyfromthePRAMmodelitisusuallyassumedthatthenumberofsuperstepsshouldbepolylogarithmicinP,butthereseemstobenorealworldrationaleforthat.Infact,algorithmsthatsimplyensureanumberofsuperstepsthatareafunctionofP(andnotofN)performquitewellinpractice,seeGoudreauetal.[10].InthispaperwedescribeaCGM(CoarseGrainedMulticomputers)solutiontotheLongestRepeatedSuffixEndingatEachPointinaWord(LRSE)problem.Inthismodel,weusePprocessorsforsolvingtheLRSEproblemforawordAoflengthNonanalphabetΣ.Thepaperisorganizedasfollows.IntheSection2,wepresentbackgroundneededfortheLRSEproblem.TheCGMsolutionoftheproblemisdescribedinSection3.Section4presentssomeexperimentalresultsandtheconclusionendsthepaper.
2Background2.1BasicdefinitionsandnotationsDefinition1.AstringorwordisasequenceofzeroormoresymbolsfromanalphabetΣ;thestringwithzerosymbolsisdenotedbyε.
Definition2.ThesetofallstringsoverthealphabetΣisdenotedbyΣ∗.Definition3.AstringAoflengthN(|A|=N)isrepresentedbyA[0]...A[N−1],whereA[i]∈Σfor0≤i≤N−1.
Definition4.AstringWisasubstring(orsub-word)ofAifA=UWVforU,V∈Σ∗;weequivalentlysaythatthestringWoccursatposition|U|+1inthestringA.
Definition5.Theposition|U|+1issaidtobethestartingpositionofWinAandtheposition|U|+|W|theendingpositionofWinA.WedenoteW=A[|U|+1...|U|+|W|].ACGMAlgorithmfortheLRSEProblem3Definition6.AstringWisaprefixofAifA=WUforU∈Σ∗.Similarly,WisasuffixofAifA=UWforU∈Σ∗.
2.2DynamicprogrammingapproachLetA=A[0...N−1]beawordoflengthNonanalphabetΣ.Wedefineatwo-dimensionaltableTasfollows:
T[i,j]=max{ℓ|A[i−ℓ+1...i]=A[j−ℓ+1...j]}for0≤j≤N−1and0≤icommonsuffixofA[0...i]andA[0...j].Figure1givesanexampleoftableT.
j01234567891011iabbcabcdabcd−1ε0000000000000a000100010001b10020002002b0010001003c002000204a00010005b0002006c000307d00048a0009b0010d0
Fig.1.ValuesofthetableTforA=abbcabcdabcd.ThefollowinglemmashowshowtocomputethevaluesofthetableT.Lemma1.ThevaluesofthetableTcanbecomputedusingthefollowingre-currenceformula:
T[−1,j]=0for0≤j≤N−1(1)andT[i,j]=T[i−1,j−1]+1ifA[i]=A[j]0otherwise(2)for0≤j≤N−1and0≤iProof.See[12].4ThierryGarciaandDavidSem´eA[i]abacacS[i]011213
Pelements.Figure3givesanexampleofthecut-tableT′.Cut-tableT′containstwokindofparts:triangularsub-tables(TT)andsquaresub-tables(ST).Lemma1canbeappliedontriangularsub-tablesbecauseofthecomparisonofasubstringofAcalledA1withitself.Thefollowinglemmashowshowtocomputethevaluesofasquaresub-tableSTfromthecomparisonbetweenA1andA2,twodifferentsubstringsofA.
Lemma3.Thevaluesofthesub-tableSTcanbecomputedusingthefollowingrecurrenceformula:
ST[−1,j]=0for−1≤j≤N−1(4)ST[i,−1]=0for0≤i≤N−1(5)ACGMAlgorithmfortheLRSEProblem5j0123891011iabbcabcd10000200010000204a10005b02006c00307d00046ThierryGarciaandDavidSem´ewhereCandLarerespectivelythelastcolumnandthelastrowofthepreviousparttableofthecuttable.Thefollowingsectiondescribestwosequentialalgorithmbasedonthediffer-entlemmas,whichareusedinourCGMalgorithm.
3.1SequentialalgorithmAlgorithm1computesthetriangularcut-tableTT,columnbycolumnandcon-structthetableSbyusingthelemmas1and2.Attheend,thealgorithmkeepsthelastcolumninthetableC.
Algorithm1for(i=2)to(i=N)for(j=1)to(j=i-1)TEMPC[j]=0if(A[i]=A[j])thenif(j=1)thenTEMPC[j]=L[i-1]+1elseTEMPC[j]=C[j-1]+1endifif(TEMPC[j]>S[i])thenS[i]=TEMPC[j]endifendifendforfor(j=1)to(j=i-1)C[j]=TEMPC[j]endforendfor
Algorithm2computesthesquarecut-tableST,columnbycolumnandcon-structthetableSbyusingthelemmas1and2.Attheend,thealgorithmkeepsthelastrowinthetableLandthelastcolumninthetableC.ThefirstelementofthetableListhelastelementofthepreviouscolumnC.