Escaping a Grid by Edge-Disjoint Paths

We present a technique for designing external memory data structures that support batched operations I/ O efficiently. We show how the technique can be used to develop external versions of a search tree, a priority queue, and a segment tree, and give examples of how these structures can be used to develop I/ O-efficient algorithms. The developed algorithms are either extremely simple or straightforward generalizations of known internal memory algorithms—given the developed external data structures.     

Finding Edge-Disjoint Paths in Partial k -Trees

For a given graph G and p pairs (s _i ,t _i ) , , of vertices in G , the edge-disjoint paths problem is to find p pairwise edge-disjoint paths P _i , , connecting s _i and t _i . Many combinatorial problems can be efficiently solved for partial k -trees (graphs of treewidth bounded by a fixed integer k ), but the edge-disjoint paths problem is NP-complete even for partial 3 -trees. This paper gives two algorithms for the edge-disjoint paths problem on partial k -trees. The first one solves the problem for any partial k -tree G and runs in polynomial time if p=O( log n) and in linear time if p=O(1) , where n is the number of vertices in G . The second one solves the problem under some restriction on the location of terminal pairs even if . Received January 21, 1977; revised September 19, 1997.     

A Fully Dynamic Approximation Scheme for Shortest Paths in Planar Graphs

In this paper we give a fully dynamic approximation scheme for maintaining all-pairs shortest paths in planar networks. Given an error parameter such that , our algorithm maintains approximate all-pairs shortest paths in an undirected planar graph G with nonnegative edge lengths. The approximate paths are guaranteed to be accurate to within a 1+ factor. The time bounds for both query and update for our algorithm is O( ^-1 n ^2/3 log ² n log D) , where n is the number of nodes in G and D is the sum of its edge lengths. The time bound for the queries is worst case, while that for the additions is amortized. Our approximation algorithm is based upon a novel technique for approximately representing all-pairs shortest paths among a selected subset of the nodes by a sparse substitute graph. Received January 1995; revised February 1997.     

Uniquely Restricted Matchings

A matching in a graph is a set of edges no two of which share a common vertex. In this paper we introduce a new, specialized type of matching which we call uniquely restricted matchings, originally motivated by the problem of determining a lower bound on the rank of a matrix having a specified zero/ non-zero pattern. A uniquely restricted matching is defined to be a matching M whose saturated vertices induce a subgraph which has only one perfect matching, namely M itself. We introduce the two problems of recognizing a uniquely restricted matching and of finding a maximum uniquely restricted matching in a given graph, and present algorithms and complexity results for certain special classes of graphs. We demonstrate that testing whether a given matching M is uniquely restricted can be done in O(|M||E|) time for an arbitrary graph G=(V,E) and in linear time for cacti, interval graphs, bipartite graphs, split graphs and threshold graphs. The maximum uniquely restricted matching problem is shown to be NP-complete for bipartite graphs, split graphs, and hence for chordal graphs and comparability graphs, but can be solved in linear time for threshold graphs, proper interval graphs, cacti and block graphs. Received April 12, 1998; revised June 21, 1999.     

Output-Sensitive Reporting of Disjoint Paths

A k -path query on a graph consists of computing k vertex-disjoint paths between two given vertices of the graph, whenever they exist. In this paper we study the problem of performing k -path queries, with , in a graph G with n vertices. We denote with the total length of the reported paths. For , we present an optimal data structure for G that uses O(n) space and executes k -path queries in output-sensitive time. For triconnected planar graphs, our results make use of a new combinatorial structure that plays the same role as bipolar (st ) orientations for biconnected planar graphs. This combinatorial structure also yields an alternative construction of convex grid drawings of triconnected planar graphs. Received August 24, 1996; revised April 8, 1997.     

Two fixed-parameter algorithms for Vertex Covering by Paths on Trees

Vertex Covering by Paths on Trees with applications in machine translation is the task to cover all vertices of a tree T=(V,E) by choosing a minimum-weight subset of given paths in the tree. The problem is NP-hard and has recently been solved by an exact algorithm running in O(C⁴⋅²|V|) time, where C denotes the maximum number of paths covering a tree vertex. We improve this running time to O(C²⋅C⋅|V|). On the route to this, we introduce the problem Tree-like Weighted Hitting Set which might be of independent interest. In addition, for the unweighted case of Vertex Covering by Paths on Trees, we present an exact algorithm using a search tree of size O(k²⋅k!), where k denotes the number of chosen covering paths. Finally, we briefly discuss the existence of a size-O(k²) problem kernel.     

Maintaining Spanning Trees of Small Diameter

Given a graph G with m edges and n nodes, a spanning tree T of G , and an edge e that is being deleted from or inserted into G , we give efficient O(n) algorithms to compute a possible swap for e that minimizes the diameter of the new spanning tree. This problem arises in high-speed networks, particularly in optical networks. Received January 1995; revised February 1997.     

Improved Algorithms for Dynamic Shortest Paths

We describe algorithms for finding shortest paths and distances in outerplanar and planar digraphs that exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge can be deleted. In the case of outerplanar digraphs, our data structures can be updated after any such change in only logarithmic time. A distance query is also answered in logarithmic time. In the case of planar digraphs, we give an interesting tradeoff between preprocessing, query, and update times depending on the value of a certain topological parameter of the graph. Our results can be extended to n -vertex digraphs of genus O(n ^1-ε ) for any ε>0 . Received September 24, 1996; revised May 13, 1998, and January 20, 1999.     

Maintaining the Classes of 4-Edge-Connectivity in a Graph On-Line

Two vertices of an undirected graph are called k -edge-connected if there exist k edge-disjoint paths between them (equivalently, they cannot be disconnected by the removal of less than k edges from the graph). Equivalence classes of this relation are called classes of k -edge-connectivity or k -edge-connected components. This paper describes graph structures relevant to classes of 4 -edge-connectivity and traces their transformations as new edges are inserted into the graph. Data structures and an algorithm to maintain these classes incrementally are given. Starting with the empty graph, any sequence of q Same-4-Class? queries and n Insert-Vertex and m Insert-Edge updates can be performed in O(q + m + n log n) total time. Each individual query requires O(1) time in the worst-case. In addition, an algorithm for maintaining the classes of k -edge-connectivity (k arbitrary) in a (k-1) -edge-connected graph is presented. Its complexity is O(q + m + n) , with O(M +k ² n log (n/k)) preprocessing, where M is the number of edges initially in the graph and n is the number of its vertices. Received July 5, 1995; revised October 21, 1996.     

Separators in Graphs with Negative and Multiple Vertex Weights

A separator theorem for a class of graphs asserts that every graph in the class can be divided approximately in half by removing a set of vertices of specified size. Nontrivial separator theorems hold for several classes of graphs, including graphs of bounded genus and chordal graphs. We show that any separator theorem implies various weighted separator theorems. In particular, we show that if the vertices of the graph have real-valued weights, which may be positive or negative, then the graph can be divided exactly in half according to weight. If k unrelated sets of weights are given, the graph can be divided simultaneously by all k sets of weights. These results considerably strengthen earlier results of Gilbert, Lipton, and Tarjan: (1) for k=1 with the weights restricted to being nonnegative, and (2) for k>1 , nonnegative weights, and simultaneous division within a factor of (1+ε ) of exactly in half. Received November 21, 1995; revised October 30, 1997.     

Randomized local elections

We propose and analyze two randomized local election algorithms in an asynchronous anonymous graph.     

军事网格工作流调度算法研究

针对军事网格应用及工作流的特点,提出一种基于网格工作流分割的调度算法。采用基于有向无环图的工作流建模方法,对网格工作流的相关概念进行形式化定义。在确定基本工作流之间的复合关系后,对网格工作流中的任务实施调度。实例结果表明,该算法能减少网格工作流的任务执行时间,具有较好的调度性能。     

A clique-covering sufficient condition for hamiltonicity of graphs

A graph is hamiltonian if it contains a cycle which goes through all vertices exactly once. Determining if a graph is hamiltonian is known as NP-complete problem and no satisfactory characterization for hamiltonian graphs has been found. There are several necessary conditions for hamiltonicity and since the seminal work of Dirac in 1952, many sufficient conditions were found. These conditions are usually expressed in terms of node degree, connectivity, density, toughness, independent sets, regularity and forbidden subgraphs. In this article we give an extended clique decomposition condition ensuring the hamiltonicity of a large class of graphs. Then we discuss briefly the possibility of broader extensions as well as algorithmic issues.     

一个大型实时数据自动检测系统图形界面的设计

该文介绍一个大型实时数据自动检测系统图形界面的设计方法，根据系统多任务、多软件环境、长时间在线实时检测的特点，合理地设定各任务的具体工作内容及其前后台属性，以优化准则设计各任务的连接规程和程序的运行要求，使图形界面为系统的实时监测快速而准确地提供各种图形图表手段。     

输出图的全部Hamiltonian回路的新算法

为求出图的全部哈密顿回路,本文提出了H集合、连接积、H矩阵和通路矩阵等概念。给出了基于这些概念下的一些哈密顿回路的存在性判定定理和通过构造通路矩阵序列Mk=Mk-1*M(k=2,...,n)的办法输出简单图（无向或有向）的全部哈密顿回路的算法和实例。本算法特别适合寻找图的最短哈密顿回路,较其它算法更为简单直观。     

非固定连接卫星星座路径选择算法稳定性分析

与传统的相对固定的卫星网络拓扑不同,基于非固定方式连接的卫星网络,由于具有更加灵活的网络组织方式,以及卓越的抗毁性等优点,正在被越来越多地研究.针对这种网络,首先进行了抽象化的表述:通过最短路径算法递归搜索整个问题空间从而得到全状态空间,并且对链路切换这一概念给出了严格的数学定义.基于此种抽象化的过程,对问题空间赋予3种不同的权值,分析比较了各种权值在最短路径算法下的稳定性,用计算机仿真结果进行比较,论证了理论分析的正确性,为探索非固定方式连接的卫星网络算法移植的可能性进行了尝试.     

Worst case analysis of a greedy algorithm for graph thickness

In this paper, we consider a greedy algorithm for thickness of graphs. The greedy algorithm we consider here takes a maximum planar subgraph away from the current graph in each iteration and repeats this process until the current graph has no edge. The greedy algorithm outputs the number of iterations which is an upper bound of thickness for an input graph G=(V,E). We show that the performance ratio of the greedy algorithm is .     

Parallel Mesh Algorithms for Grid Graph Shortest Paths with Application to Separation of Touching Chromosomes

The grid graph shortest path problem has many applications. In this paper, we present practical mesh algorithms using a local cost-reducing operation for various forms of the grid graph shortest path problem. The algorithms are very simple and can easily mark the vertices on shortest paths between any two vertices. The time complexity of the algorithm is proportional to the maximum length of the shortest paths with a very small multiplicative constant. Also in this paper, we discuss the application of the parallel algorithms in automatic chromosome analysis to intelligently split touching chromosomes. We identify local features useful for finding a potential path to separate touching chromosomes. We then define a distance measure based on the local features and find the best splitting path to cut touching chromosomes. The splitting algorithm only uses local information and is highly parallel.     

Formal Derivation of Graph AlgorithmicPrograms Using Partition-and-Recur

In this paper,we derive,by presenting some suitable notations,three typical graph algorithms and corresponding programs using a unified approach,partition-and-recur.We putemphasis on the derivation rather than the algorithms themselves.The main ideas and ingenuity of these algorithms are revealed by formula deduction.Success in these examples gives us more evidence that partition-and-recur is a simple and practical approach and developing enough suitable notations is the key in designing and deriving efficient and correct algorithmic programs.     

服务质量感知的网格工作流调度

在网格工作流中引入服务质量,可以使网格中的资源更好地围绕用户的要求进行组织和分配,服务质量为工作流执行过程中选择成员服务提供了依据.工作流服务质量的估算和服务质量感知的工作流调度是实现服务质量感知的网格工作流的两个关键问题.基于一种网格工作流模型讨论了网格工作流的服务质量参数体系,提出了工作流服务质量的估算算法和网格工作流调度数学模型,并提出了基于遗传算法的调度方法.仿真实验表明,该调度算法具有较好的收敛性.