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ON THE STRUCTURE OF MINIMUMWEIGHT kCONNECTED SPANNING NETWORKS
, 1990
"... The problem offinding a minimumweight kconnected spanning subgraph ofa complete graph, assuming that the edge weights satisfy the triangle inequality, is studied. It is shown that the class of minimumweight kedge connected spanning subgraphs can be restricted to those subgraphs which, in additi ..."
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Cited by 21 (2 self)
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The problem offinding a minimumweight kconnected spanning subgraph ofa complete graph, assuming that the edge weights satisfy the triangle inequality, is studied. It is shown that the class of minimumweight kedge connected spanning subgraphs can be restricted to those subgraphs which
The longest path problem is polynomial on cocomparability graphs
 ALGORITHMICA
"... The longest path problem is the problem of finding a path of maximum length in a graph. As a generalization of the Hamiltonian path problem, it is NPcomplete on general graphs and, in fact, on every class of graphs that the Hamiltonian path problem is NPcomplete. Polynomial solutions for the longe ..."
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Cited by 5 (0 self)
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The longest path problem is the problem of finding a path of maximum length in a graph. As a generalization of the Hamiltonian path problem, it is NPcomplete on general graphs and, in fact, on every class of graphs that the Hamiltonian path problem is NPcomplete. Polynomial solutions
Longest paths in circular arc graphs
 Combin. Probab. Comput
"... Abstract. We show that all maximum length paths in a connected circular arc graph have a nonempty intersection. ..."
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Cited by 7 (0 self)
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Abstract. We show that all maximum length paths in a connected circular arc graph have a nonempty intersection.
LONGEST PATH DISTANCE IN RANDOM CIRCUITS
"... ABSTRACT. We study distance properties of a general class of random directed acyclic graphs (DAGs). In a DAG, many natural notions of distance are possible, for there exists multiple paths between pairs of nodes. The distance of interest for circuits is the maximum length of a path between two nodes ..."
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ABSTRACT. We study distance properties of a general class of random directed acyclic graphs (DAGs). In a DAG, many natural notions of distance are possible, for there exists multiple paths between pairs of nodes. The distance of interest for circuits is the maximum length of a path between two
Finding a longest path in a complete multipartite digraph
 SIAM J. DISCRETE MATH
, 1993
"... A digraph obtained by replacing each edge of a complete mpartite graph with an arc or a pair of mutually opposite arcs with the same end vertices is called a complete mpartite digraph. We describe an O(n 3) algorithm for finding a longest path in a complete mpartite (m ≥ 2) digraph with n vertic ..."
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Cited by 18 (10 self)
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A digraph obtained by replacing each edge of a complete mpartite graph with an arc or a pair of mutually opposite arcs with the same end vertices is called a complete mpartite digraph. We describe an O(n 3) algorithm for finding a longest path in a complete mpartite (m ≥ 2) digraph with n
The Longest Path Problem on Permutation Graphs
 THE 29TH WORKSHOP ON COMBINATORIAL MATHEMATICS AND COMPUTATION THEORY
"... The longest path problem on graph G is a classic problem which is to find a simple path such that the number of vertices of the path is maximum among all possible paths of G. In this paper, we show that the longest path problem can be solved in linear time on permutation graphs. ..."
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The longest path problem on graph G is a classic problem which is to find a simple path such that the number of vertices of the path is maximum among all possible paths of G. In this paper, we show that the longest path problem can be solved in linear time on permutation graphs.
28 A DISTRIBUTED SYNCHRONOUS ALGORITHM FOR MINIMUMWEIGHT SPANNING TREES
"... Abstract: This paper presents a distributed synchronous algorithm for constructing the MinimumWeight Spanning Tree (MST) in a connected undirected graph with distinct edge weights. Each node in the graph is considered as a processor having the initial knowledge of weights of the adjacent edges and ..."
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Abstract: This paper presents a distributed synchronous algorithm for constructing the MinimumWeight Spanning Tree (MST) in a connected undirected graph with distinct edge weights. Each node in the graph is considered as a processor having the initial knowledge of weights of the adjacent edges
PerformanceEffective and LowComplexity Task Scheduling for Heterogeneous Computing
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 2002
"... Efficient application scheduling is critical for achieving high performance in heterogeneous computing environments. The application scheduling problem has been shown to be NPcomplete in general cases as well as in several restricted cases. Because of its key importance, this problem has been exte ..."
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Cited by 255 (0 self)
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with the related work, a parametric graph generator was designed to generate weighted directed acyclic graphs with various characteristics. The comparison study, based on both randomly generated graphs and the graphs of some real applications, shows that our scheduling algorithms significantly surpass previous
Linear Structure of Bipartite Permutation Graphs and the Longest Path Problem
"... The class of bipartite permutation graphs is the intersection of two well known graph classes: bipartite graphs and permutation graphs. A complete bipartite decomposition of a bipartite permutation graph is proposed in this note. The decomposition gives a linear structure of bipartite permutation gr ..."
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Cited by 6 (0 self)
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graphs, and it can be obtained in O(n) time, where n is the number of vertices. As an application of the decomposition, we show an O(n) time and space algorithm for finding a longest path in a bipartite permutation graph.
Intersection of longest paths and cycles
, 2008
"... It is a well known fact in graph theory that in a connected graph any two longest paths must have a vertex in common. In this paper we will explore what happens when we look at k − connected graphs, leading us to make a conjecture about the intersection of any two longest paths. We then look at cycl ..."
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It is a well known fact in graph theory that in a connected graph any two longest paths must have a vertex in common. In this paper we will explore what happens when we look at k − connected graphs, leading us to make a conjecture about the intersection of any two longest paths. We then look
Results 11  20
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2,088