All-Pairs Bottleneck Paths in Vertex Weighted Graphs

Let G=(V,E,w) be a directed graph, where w:V→ℝ is a weight function defined on its vertices. The bottleneck weight, or the capacity, of a path is the smallest weight of a vertex on the path. For two vertices u,v the capacity from u to v, denoted by c(u,v), is the maximum bottleneck weight of a path from u to v. In the All-Pairs Bottleneck Paths (APBP) problem the task is to find the capacities for all ordered pairs of vertices. Our main result is an O(n ^2.575) time algorithm for APBP. The exponent is derived from the exponent of fast matrix multiplication.     

Reduction Algorithms for Graphs of Small Treewidth

This paper presents a number of new ideas and results on graph reduction applied to graphs of bounded treewidth. S. Arnborg, B. Courcelle, A. Proskurowski, and D. Seese (J. Assoc. Comput. Mach.40, 1134–1164 (1993)) have shown that many decision problems on graphs can be solved in linear time on graphs of bounded treewidth, using a finite set of reduction rules. These algorithms can be used to solve problems on graphs of bounded treewidth without the need to obtain a tree decomposition of the input graph first. We show that the reduction method can be extended to solve the construction variants of many decision problems on graphs of bounded treewidth, including all problems definable in monadic second order logic. We also show that a variant of these reduction algorithms can be used to solve (constructive) optimization problems in O(n) time. For example, optimization and construction variants of I S and H C N can be solved in this way on graphs of small treewidth. Additionally, we show that the results of H. L. Bodlaender and T. Hagerup (SIAM J. Comput.27, 1725–1746 (1998)) can be applied to our reduction algorithms, which results in parallel reduction algorithms that use O(n) operations and O(log n log* n) time on an EREW PRAM, or O(log n) time on a CRCW PRAM.     

All Pairs Shortest Distances for Graphs with Small Integer Length Edges

There is a way to transform the All Pairs Shortest Distances (APSD) problem where the edge lengths are integers with small (?M) absolute value into a problem with edge lengths in {−1, 0, 1}. This transformation allows us to use the algorithms we developed earlier ([1]) and yields quite efficient algorithms. In this paper we give new improved algorithms for these problems. Forn=|V| the number of vertices,Mthe bound on edge length, andωthe exponent of matrix multiplication, we get the following results: 1. A directed nonnegative APSD(n, M) algorithm which runs inO(T(n, M)) time, where[formula]2. A undirected APSD(n, M) algorithm which runs inO(M^(ω+1)/2n^ωlog(Mn)) time.     

Fast Algorithms for Approximating Distances

In this paper we present efficient approximation algorithms for the distance selection problem. Our technique is based on the well-separated pair decomposition proposed in [8]. Received May 16, 1999; revised June 5, 2001.     

Many Distances in Planar Graphs

We show how to compute in O(n ^4/3log?^1/3 n+n ^2/3 k ^2/3log?n) time the distance between k given pairs of vertices of a planar graph G with n vertices. This improves previous results whenever (n/log?n)^5/6≤k≤n ²/log?⁶ n. As an application, we speed up previous algorithms for computing the dilation of geometric planar graphs.     

Approximation Algorithms for Average Stretch Scheduling

We study the basic problem of preemptive scheduling of a stream of jobs on a single processor. Consider an on-line stream of jobs, and let the ith job arrive at time r(i) and have processing time p(i). If C(i) is the completion time of job i, then the flow time of i is C(i) − r(i) and the stretch of i is the ratio of its flow time to its processing time; that is, . Flow time measures the time that a job is in the system regardless of the service it requests; the stretch measure relies on the intuition that a job that requires a long service time must be prepared to wait longer than jobs that require small service times. We present the improved algorithmic results for the average stretch metric in preemptive uniprocessor scheduling. Our first result is an off-line polynomial-time approximation scheme (PTAS) for average stretch scheduling. This improves upon the 2-approximation achieved by the on-line algorithm srpt that always schedules a job with the shortest remaining processing time. In a recent work, Chekuri and Khanna (Proc. 34th Ann. Symp. Theory Comput., 297–305, 2002) have presented approximation algorithms for weighted flow time, which is a more general metric than average stretch; their result also yields a PTAS for average stretch. Our second set of results considers the impact of incomplete knowledge of job sizes on the performance of on-line scheduling algorithms. We show that a constant-factor competitive ratio for average stretch is achievable even if the processing times (or remaining processing times) of jobs are known only to within a constant factor of accuracy.     

Faster Algorithms for Stable Allocation Problems

We consider a high-multiplicity generalization of the classical stable matching problem known as the stable allocation problem, introduced by Baïou and Balinski in 2002. By leveraging new structural properties and sophisticated data structures, we show how to solve this problem in O(mlog?n) time on a bipartite instance with n vertices and m edges, improving the best known running time of O(mn). Building on this algorithm, we provide an algorithm for the non-bipartite stable allocation problem running in O(mlog?n) time with high probability. Finally, we give a polynomial-time algorithm for solving the “optimal” variant of the bipartite stable allocation problem, as well as a 2-approximation algorithm for the NP-hard “optimal” variant of the non-bipartite stable allocation problem.     

Approximation Algorithms for Intersection Graphs

We study three complexity parameters that, for each vertex v, are an upper bound for the number of cliques that are sufficient to cover a subset S(v) of its neighbors. We call a graph k-perfectly groupable if S(v) consists of all neighbors, k-simplicial if S(v) consists of the neighbors with a higher number after assigning distinct numbers to all vertices, and k-perfectly orientable if S(v) consists of the endpoints of all outgoing edges from v for an orientation of all edges. These parameters measure in some sense how chordal-like a graph is—the last parameter was not previously considered in literature. The similarity to chordal graphs is used to construct simple polynomial-time approximation algorithms with constant approximation ratio for many NP-hard problems, when restricted to graphs for which at least one of the three complexity parameters is bounded by a constant. As applications we present approximation algorithms with constant approximation ratio for maximum weighted independent set, minimum (independent) dominating set, minimum vertex coloring, maximum weighted clique, and minimum clique partition for large classes of intersection graphs.     

空间数据库中最小距离聚集查询及其算法

提出了一种新的距离查询形式-最小距离聚集查询,这种查询计算几个对象集中对象到一个中心对象集中对象的距离和,并返回最小的K个距离和.在空间数据库中,对基于R树索引的数据集给出了基于最近邻居的方法和阈值算法来回答查询.通过大量实验对两种算法进行了比较,结果显示阈值算法具有较好的性能.     

带权图的多重分形度量

分形维数及多重分形是分形理论的重要研究内容.复杂网络的多重分形已经得到了较为深入的研究,但对复杂网络多重分形的度量目前并没有可行的方法.带权图是复杂网络研究的重要对象,其中的节点权重及边权重可以为正实数、负实数、纯虚数及复数等多种不同的类型.除节点权重及边权重均为正实数的情形外,其他类型的带权图都具有多重分形特性,且均...     

带权图的均衡k划分

带权图的均衡k划分是把一个图的顶点集分成k个不相交的子集,使得任意2个子集中顶点的权值之和的差异达到极小,并且连接不同子集的边权之和也达到极小.这种图的k划分问题已被应用在软硬件协同设计、大规模集成电路设计和数据划分等领域,它已被证明是NP完全问题.首先针对带权图的均衡k划分问题提出了能够生成优质近似解的启发式算法.该算法在保证子集均衡的条件下,采用最大化同一子集内部边权之和的策略来构造每一个顶点子集;构建子集S的思想是每次从候选集中选择与子集S相连的具有最大增益的顶点放入子集S中,直到子集S的顶点权值之和满足要求.此外,采用了定制的禁忌搜索算法对生成的初始近似解实施进一步优化.实验结果表明,当k分别取值为2,4,8时所提算法分别在86%,81%,68%的基准图上求得的平均解优于当前最新算法求得的平均解;解的最大改进幅度可达60%以上.     

Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs

Hierarchical graphs and clustered graphs are useful non-classical graph models for structured relational information. Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in CASE tools, software visualization and VLSI design. Drawing algorithms for hierarchical graphs have been well investigated. However, the problem of planar straight-line representation has not been solved completely. In this paper we answer the question: does every planar hierarchical graph admit a planar straight-line hierarchical drawing? We present an algorithm that constructs such drawings in linear time. Also, we answer a basic question for clustered graphs, that is, does every planar clustered graph admit a planar straight-line drawing with clusters drawn as convex polygons? We provide a method for such drawings based on our algorithm for hierarchical graphs.     

Efficient Parallel Algorithms for Permutation Graphs

In this paper, we present optimal O(log n) time, O(n/log n) processor EREW PRAM parallel algorithms for finding the connected components, cut vertices, and bridges of a permutation graph. We also present an O(log n) time, O(n) processor, CREW PRAM model parallel algorithm for finding a Breadth First Search (BFS) spanning tree of a permutation graph rooted at vertex 1 and use the same to derive an efficient parallel algorithm for the All Pairs Shortest Path problem on permutation graphs.     

Exact Algorithms for Intervalizing Coloured Graphs

In the Intervalizing Coloured Graphs problem, one must decide for a given graph G = (V, E) with a proper vertex colouring of G whether G is the subgraph of a properly coloured interval graph. For the case that the number of colors is fixed, we give an exact algorithm that uses \(2^{\mathcal {O}(n/\log n)}\) time. We also give an \(\mathcal {O}^{\ast }(2^{n})\) algorithm for the case that the number of colors is not fixed.     

入侵检测中的快速过滤算法

入侵检测系统是近年来发展迅速的一种网络安伞技术。但是,随着计算机网络向着高速、宽带的方向发展，检测引擎越来越成为性能的瓶颈.如果检测速度不能跟上网络流最，就会丢包并发生漏报。这除了采用更高速的专业硬件来解决外，包过滤算法也有非常重要的作用，高述的过滤算法有助于过滤掉大量无关的信息，从而极大地提高入侵检测系统的性能。     

加权3D-Matching的改进算法

Matching问题构成了一类重要的NP难问题.此类问题在诸多领域中有着重要的应用,如调度、代码优化等领域.对于加权3D-matching问题,通过深入分析问题的结构特性,可以转化成加权3D-matching augmentation问题进行求解,即从一个最大加权的k-matching着手构造权值最大的(k+1)-matching.从问题的特殊结构特性出发,给出了加权3D-matching augmentation问题特有的性质: k- matching中存在2列使得该2列至少有2k/3元素被包含在(k+1)-matching中所对应的2列中.基于给出的性质,通过运用color-coding和动态规划技术,给出了一个时间复杂度为O* (4.823k)的参数算法,最终求解加权3D-matching问题.该算法较目前文献中的最好结果O* (5.473k)有了极大的改进.