背包问题的最优并行算法

利用分治策略,提出一种基于SIMD共享存储计算机模型的并行背包问题求解算法.算法允许使用O(2^n/4)^1-ε个并行处理机单元,0≤ε≤1,O(2^n/2)个存储单元,在O(2^n/4(2^n/4)^ε)时间内求解n维背包问题,算法的成本为O(2^n/2).将提出的算法与已有文献结论进行对比表明,该算法改进了已有文献的相应结果,是求解背包问题的成本最优并行算法.同时还指出了相关文献主要结论的错误.     

背包类问题的并行O(25n/6)时间-空间-处理机折衷

将串行动态二表算法应用于并行三表算法的设计中,提出一种求解背包、精确的可满足性和集覆盖等背包类NP完全问题的并行三表六子表算法.基于EREW-PRAM模型,该算法可使用O(2n/8)的处理机在O(27n/16)的时间和O(213n/48)的空间求解n维背包类问题,其时间-空间-处理机折衷为O(25n/6).与现有文献的性能对比分析表明,该算法极大地提高了并行求解背包类问题的时间-空间-处理机折衷性能.由于该算法能够破解更高维数的背包类公钥和数字水印系统,其结论在密钥分析领域具有一定的理论和实际意义.     

具有O(n)消息复杂度的协调检查点设置算法

协调检查点设置及回卷恢复技术作为一种有效的容错手段,已广泛地运用在集群等并行/分布计算机系统中.为了进一步降低协调检查点设置的时间和空间开销,提出了一种基于消息计数的协调检查点设置算法.该算法无须对底层消息通道的FIFO特性进行假设,并使同步阶段引入的控制消息复杂度由通常的O(n²)降低到O(n),有效地提高了系统的效率和扩展性.     

模糊聚类计算的最佳算法

给出模糊关系传递闭包在对应模糊图上的几何意义,并提出一个基于图连通分支计算的模糊聚类最佳算法.对任给的n个样本,新算法最坏情况下的时间复杂性函数T(n)满足O(n)≤T(n)≤O(n²).与经典的基于模糊传递闭包计算的模糊聚类算法的O(n³logn)计算时间相比,新算法至少降低了O(n相似文献   

虫孔路由Mesh上的连通分量算法及其应用

用倍增技术在带有Wormhole路由技术的n×n二维网孔机器上提出了时间复杂度为O(log²n)的连通分量和传递闭包并行算法,并在此基础上提出了一个时间复杂度为O(log³n)的最小生成树并行算法.这些都改进了Store-and-Forward路由技术下的时间复杂度下界O(n).同其他运行在非总线连接分布式存储并行计算机上的算法相比,此连通分量和传递闭包算法的时间复杂度是最优的.     

确定任意多边形凸凹顶点的算法

本文提出一种确定任意多边形凸凹顶点的算法．该算法的时间复杂性为O(n²logn)次乘法和O(n²)次比较．     

双向选择排序算法

为丰富O(n²)阶排序算法的种类,以更好地服务于教学科研和日常应用,提出了一种新的排序算法-双向选择排序算法.通过数学方法分析得知:该算法的时间复杂度为O(n²),空间复杂度为O(1).通过实验对比得知:在相同条件下,该算法的运行时间平均为冒泡排序的27%、简单选择排序的62%、直接插入排序的88%.     

光RP(k)网络上Hypercube通信模式的波长指派算法

波长指派是光网络设计的基本问题,设计波长指派算法是洞察光网络通信能力的基本方法.基于光RP(k)网络,讨论了其波长指派问题. 含有N=2ⁿ个节点的Hypercube通信模式,构造了节点间的一种排列次序Xn,并设计了RP(k)网络上的波长指派算法.在构造该算法的过程中,得到了在环网络上实现n维Hypercube通信模式的波长指派算法.这两个算法具有较高的嵌入效率.在RP(k)网络上,实现Hypercube通信模式需要max{2,「5(2^n-5/3」}个波长.而在环网络上,实现该通信模式需要复用(N/3+N/12(个波长,比已有算法需要复用「N/3+N/4」个波长有较大的改进.这两个算法对于光网络的设计具有较大的指导价值.     

求解大规模谱聚类的近似加权核k-means算法

谱聚类将聚类问题转化成图划分问题,是一种基于代数图论的聚类方法.在求解图划分目标函数时,一般利用Rayleigh熵的性质,通过计算Laplacian矩阵的特征向量将原始数据点映射到一个低维的特征空间中,再进行聚类.然而在谱聚类过程中,存储相似矩阵的空间复杂度是O(n²),对Laplacian矩阵特征分解的时间复杂度一般为O(n³),这样的复杂度在处理大规模数据时是无法接受的.理论证明,Normalized Cut图聚类与加权核k-means都等价于矩阵迹的最大化问题.因此,可以用加权核k-means算法来优化Normalized Cut的目标函数,这就避免了对Laplacian矩阵特征分解.不过,加权核k-means算法需要计算核矩阵,其空间复杂度依然是O(n²).为了应对这一挑战,提出近似加权核k-means算法,仅使用核矩阵的一部分来求解大数据的谱聚类问题.理论分析和实验对比表明,近似加权核k-means的聚类表现与加权核k-means算法是相似的,但是极大地减小了时间和空间复杂性.     

一类可分离SAT问题的O(1.890n)精确算法

布尔可满足性问题（SAT）是指对于给定的布尔公式,是否存在一个可满足的真值指派.这是第1个被证明的NP完全问题,一般认为不存在多项式时间算法,除非P=NP.学者们大都研究了子句长度不超过k的SAT问题（k-SAT）,从全局搜索到局部搜索,给出了大量的相对有效算法,包括随机算法和确定算法.目前,最好算法的时间复杂度不超过O（（2-2/k）ⁿ）,当k=3时,最好算法时间复杂度为O（1.308ⁿ）.而对于更一般的与子句长度k无关的SAT问题,很少有文献涉及.引入了一类可分离SAT问题,即3-正则可分离可满足性问题（3-RSSAT）,证明了3-RSSAT是NP完全问题,给出了一般SAT问题3-正则可分离性的O（1.890ⁿ）判定算法.然后,利用矩阵相乘算法的研究成果,给出了3-RSSAT问题的O（1.890ⁿ）精确算法,该算法与子句长度无关.     

Efficient parallel and sequential algorithms for 4-coloring perfect planar graphs

We present an efficient algorithm for 4-coloring perfect planar graphs. The best previously known algorithm for this problem takesO(n ^3/2) sequential time, orO(log⁴ n) parallel time withO(n³) processors. The sequential implementation of our algorithm takesO(n logn) time. The parallel implementation of our algorithm takesO(log³ n) time withO(n) processors on a PRAM.     

Efficient parallel and sequential algorithms for 4-coloring perfect planar graphs

We present an efficient algorithm for 4-coloring perfect planar graphs. The best previously known algorithm for this problem takesO(n ^3/2) sequential time, orO(log⁴ n) parallel time withO(n³) processors. The sequential implementation of our algorithm takesO(n logn) time. The parallel implementation of our algorithm takesO(log³ n) time withO(n) processors on a PRAM.

     

Searching a Polygonal Region by a Boundary Searcher

This paper considers the problem of planning the motion of a searcher in a polygonal region to eventually"see"an intruder that is unpredictable and capable of moving arbitrarily fast.A searcher is called the boundary searcher if he continuously moves on the polygon boundary and can see only along the rays of the flashlights he holds at a time. We present necessary and sufficient conditions for an n-sided polygon to be searchable by a boundary searcher.Based on our characterization,the equivalence of the ...     

Efficient parallel algorithms forr-dominating set andp-center problems on trees

We develop efficient parallel algorithms for ther-dominating set and thep-center problems on trees. On a concurrent-read exclusive-write PRAM, our algorithm for ther-dominating set problem runs inO(logn log logn) time withn processors. The algorithm for thep-center problem runs inO(log² n log logn) time withn processors.Xin He was supported in part by an Ohio State University Presidential Fellowship, and by the Office of Research and Graduate Studies of Ohio State University. Yaacov Yesha was supported in part by the National Science Foundation under Grant No. DCR-8606366.     

Improved algorithms for finding length-bounded two vertex-disjoint paths in a planar graph and minmax k vertex-disjoint paths in a directed acyclic graph

This paper is composed of two parts. In the first part, an improved algorithm is presented for the problem of finding length-bounded two vertex-disjoint paths in an undirected planar graph. The presented algorithm requires O(n³bmin) time and O(n²bmin) space, where bmin is the smaller of the two given length bounds. In the second part of this paper, we consider the minmax k vertex-disjoint paths problem on a directed acyclic graph, where k?2 is a constant. An improved algorithm and a faster approximation scheme are presented. The presented algorithm requires O(nk+1Mk−1) time and O(nkMk−1) space, and the presented approximation scheme requires O((1/?)^k−1n2klogk−1M) time and O((1/?)^k−1n2k−1logk−1M) space, where ? is the given approximation parameter and M is the length of the longest path in an optimal solution.     

RNA二级结构预测中动态规划的优化和有效并行

基于最小自由能模型的方法是计算生物学中RNA二级结构预测的主要方法,而计算最小自由能的动态规划算法需要O(n⁴)的时间,其中n是RNA序列的长度.目前有两种降低时间复杂度的策略:限制二级结构中内部环的大小不超过k,得到O(n²×k²)算法;Lyngso方法根据环的能量规则,不限制环的大小,在O(n3)的时间内获得近似最优解.通过使用额外的O(n)的空间,计算内部环中的冗余计算大为减少,从而在同样不限制环大小的情况下,在O(n³)的时间内能够获得最优解.然而,优化后的算法仍然非常耗时,通过有效的负载平衡方法,在机群系统上实现并行程序.实验结果表明,并行程序获得了很好的加速比.     

Efficient parallel solutions to some geometric problems

This paper presents new algorithms for solving some geometric problems on a shared memory parallel computer, where concurrent reads are allowed but no two processors can simultaneously attempt to write in the same memory location. The algorithms are quite different from known sequential algorithms, and are based on the use of a new parallel divide-and-conquer technique. One of our results is an O(log n) time, O(n) processor algorithm for the convex hull problem. Another result is an O(log n log log n) time, O(n) processor algorithm for the problem of selecting a closest pair of points among n input points.     

An NC algorithm for finding a minimum weighted completion time schedule on series parallel graphs

We present a parallel algorithm for solving the minimum weighted completion time scheduling problem for transitive series parallel graphs. The algorithm takesO(log² n) time withO(n ³) processors on a CREW PRAM, wheren is the number of vertices of the input graph. This is the first NC algorithm for solving the problem.Research supported in part by NSF Grants CCR-9011214 and CCR-9205982.