17202338
Fault-Free Hamiltonian Cycles in Faulty Arrangement Graphs
The arrangement graph A/sub n,k/, which is a generalization of the star graph (n-k=1), presents more flexibility than the star graph in adjusting the major design parameters: number of nodes, degree, and diameter. Previously, the arrangement graph has proved Hamiltonian. In this paper, we further show that the arrangement graph remains Hamiltonian even if it is faulty. Let |F/sub e/| and |F/sub v/| denote the numbers of edge faults and vertex faults, respectively. We show that A/sub n,k/ is Hamiltonian when 1) (k=2 and n-k/spl ges/4, or k/spl ges/3 and n-k/spl ges/4+[k/2]), and |F/sub e/|/spl les/k(n-k)-2, or 2) k/spl ges/2, n-k/spl ges/2+[k/2], and |F/sub e/|/spl les/k(n-k-3)-1, or 3) k/spl ges/2, n-k/spl ges/3, and |F/sub e/|/spl les/k, or 4) n-k/spl ges/3 and |F/sub v/|/spl les/n-3, or 5) n-k/spl ges/3 and |F/sub v/|+|F/sub e/|/spl les/k. Besides, for A/sub n,k/ with n-k=2, we construct a cycle of length at least 1) [n!/(n-k!)]-2 if |F/sub e/|/spl les/k-1, or 2) [n!/(n-k)!]-|F/sub v/|-2(k-1) if |F/sub v/|/spl les/k-1, or 3) [n!/(n-k)!]-|F/sub v/|-2(k-1) if |F/sub e/|+|F/sub v/|/spl les/k-1, where [n!/(n-k)!] is the number of nodes in A/sub n,k/.
10538824
Parallel Decomposition of Generalized Series-Parallel Graphs
Generalized series-parallel (GSP) graphs belong to the class of decomposable graphs which can be represented by their decomposition trees. Given a decomposition tree of a GSP graph, there are many graph-theoretic problems which can be solved efficiently. An efficient parallel algorithm for constructing a decomposition tree of a given GSP graph is presented. It takes O(log n) time with C(m, n) processors on a CRCW PRAM, where C(m, n) is the number of processors required to find connected components of a graph with in edges and n vertices in logarithmic time. Based on our algorithmic results, we also derive some properties for GSP graphs, which may be of interest in and of themselves.
45928902
An Efficient Parallel Strategy for Computing K-Terminal Reliability and Finding Most Vital Edges in 2-Trees and Partial 2-Trees
In this paper, we first develop a parallel algorithm for computingK-terminal reliability, denoted byR(GK), in 2-trees. Based on this result, we can also computeR(GK) in partial 2-trees using a method that transforms, in parallel, a given partial 2-tree into a 2-tree. Finally, we solve the problem of finding most vital edges with respect toK-terminal reliability in partial 2-trees. Our algorithms takeO(logn) time withC(m,n) processors on a CRCW PRAM, whereC(m,n) is the number of processors required to find the connected components of a graph withmedges andnvertices in logarithmic time.
1980858
Edge and Node Searching Problems on Trees
In this paper, we show that there is a natural correspondence between a tree's edge-search strategy and its node-search strategy. By doing so, we simplify the previous linear time algorithm for determining the edge-search number of a tree, and improve the running time of a previous algorithm for constructing an edge-search strategy (or plan) for a tree containing n vertices from O(n log n) to O(n) time.
29920941
Counting Clique Trees and Computing Perfect Elimination Schemes in Parallel
Abstract In a previous result, the authors showed that a clique tree of a chordal graph can be constructed in O(log n ) parallel computing time with O( n 3 ) processors on CRCW PRAM, where n is the number of nodes of the graph. In this paper, it will be shown that this result can be extended in two ways. First, we show that from the parallel clique tree constructing algorithm, we can derive an exact formula of counting clique trees of a labeled connected chordal graph. Next, we show that a perfect elimination scheme of a chordal graph can be computed in O(log n ) time with O( n 2 ) processors on CREW PRAM once a clique tree of the graph is given. This implies that a perfect elimination scheme of a chordal graph can be computed in O(log n ) time with O( n 3 ) processors on CRCW PRAM.
12861854
The Recognition of Geodetically Connected Graphs
Abstract Let G = ( V , E ) be a graph with vertex set V of size n and edge set E of size m . A vertex υ ϵ V is called a hinge vertex if the distance of any two vertices becomes longer after v is removed. A graph without hinge vertex is called a hinge-free graph. In general, a graph G is k -geodetically connected or k -GC for short if G can tolerate any k − 1 vertices failures without increasing the distance among all the remaining vertices. In this paper, we show that recognizing a graph G to be k -GC for the largest value of k can be solved in O ( nm ) time. In addition, more efficient algorithms for recognizing the k -GC property on some special graphs are presented. These include the O ( n + m ) time algorithms on strongly chordal graphs (if a strong elimination ordering is given), ptolemaic graphs, and interval graphs, and an O ( n 2 ) time algorithm on undirected path graphs (if a characteristic tree model is given). Moreover, we show that if the input graph G is not hinge-free then finding all hinge vertices of G can be solved in the same time complexity on the above classes of graphs.
30879352
An Ant Colony Optimization Approach to the Degree-Constrained Minimum Spanning Tree Problem
This paper presents the application of an Ant Colony Optimization (ACO) algorithm approach for communications networks design problem. We explore the use of ACO’s for solving a network optimization problem, the degree-constrained minimum spanning tree problem (d-MST), which is a NP-Hard problem. The effectiveness of the proposed algorithm is demonstrated through two kinds of data set: structured hard (SHRD) complete graphs and misleading (M-graph) complete graphs. Empirical results show that ACO performs competitively with other approaches based on evolutionary algorithm (EA) on certain instance set problem.
44418101
Degree-constrained minimum spanning tree
Abstract In this paper the problem of a degree-constrained minimum spanning tree (DCMST) is defined. The problem is formulated as a linear 0–1 integer programming problem. A primal and a dual heuristic (construction) procedure and a branch-and-bound algorithm are proposed to construct a DCMST. These procedures are illustrated with a simple example. Some computational experience with these algorithms is also reported.
39997093
Performance of an Ant Colony Optimization (ACO) Algorithm on the Dynamic Load-Balanced Clustering Problem in Ad Hoc Networks
This paper examines the performance of a recently proposed ACO algorithm when applied to the problem of constructing load-balanced clusters in ad hoc networks with node mobility. Performance, in this context, is measured in terms of the magnitude of change in solution quality after nodes move, and reactivity. Reactivity refers to the number of cycles ACO takes to recover from any degradation in solution quality resulting from node movements. Empirical results on 16 problem instances of various sizes revealed a positive correlation
34381900
Using spatial warning signals to capture a driver's visual attention
This study was designed to assess the potential benefits of using spatial auditory or vibrotactile warning signals in the domain of driving performance, using a simulated driving task. Across six experiments, participants had to monitor a rapidly presented stream of distractor letters for occasional target digits (simulating an attention-demanding visual task, such as driving). Whenever participants heard an auditory cue (E1-E4) or felt a vibration (E5-E6), they had to check the front and the rearview mirror for the rapid approach of a car from in front or behind and respond accordingly (either by accelerating or braking). The efficacy of various auditory and vibrotactile warning signals in directing a participant's visual attention to the correct environmental position was compared (see Table 1). The results demonstrate the potential utility of semantically-meaningful or spatial auditory, and/or vibrotactile warning signals in interface design for directing a driver's, or other interface-operator's, visual attention to time-critical events or information.
641485
Mapping XML and relational schemas with Clio
Merging and coalescing data from multiple and diverse sources into different data formats continues to be an important problem in modern information systems. Schema matching (the process of matching elements of a source schema with elements of a target schema) and schema mapping (the process of creating a query that maps between two disparate schemas) are at the heart of data integration systems. We demonstrate Clio, a semi-automatic schema mapping tool developed at the IBM Almaden Research Center. In this paper, we showcase Clio's mapping engine which allows mapping to and from relational and XML schemas, and takes advantage of data constraints in order to preserve data associations.