Results 1  10
of
35
The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
Abstract

Cited by 188 (0 self)
 Add to MetaCart
This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Subgraph Isomorphism in Planar Graphs and Related Problems
, 1999
"... We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small treewidth, and applying dynamic programming within each piece. The same methods can be used to ..."
Abstract

Cited by 113 (1 self)
 Add to MetaCart
We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small treewidth, and applying dynamic programming within each piece. The same methods can be used to solve other planar graph problems including connectivity, diameter, girth, induced subgraph isomorphism, and shortest paths.
Monadic second–order evaluations on treedecomposable graphs
 Theoret. Comput. Sci
, 1993
"... Courcelle, B. and M. Mosbah, Monadic secondorder evaluations on treedecomposable graphs, ..."
Abstract

Cited by 80 (23 self)
 Add to MetaCart
Courcelle, B. and M. Mosbah, Monadic secondorder evaluations on treedecomposable graphs,
Dynamic Programming On Graphs With Bounded Treewidth
, 1987
"... In this paper we study the complexity of graph decision problems, restricted to the class of graphs with treewidth _< k, (or equivalently, the class of partial ktrees), for fixed k. We introduce two classes of graph decision problems, LCC and ECC, and subclasses CLCC, and CECC. We show that each ..."
Abstract

Cited by 50 (1 self)
 Add to MetaCart
In this paper we study the complexity of graph decision problems, restricted to the class of graphs with treewidth _< k, (or equivalently, the class of partial ktrees), for fixed k. We introduce two classes of graph decision problems, LCC and ECC, and subclasses CLCC, and CECC. We show that each problem in LCC (or CLCC) is solvable in polynomial (O(nc)) time, when restricted to graphs with fixed up perbounds on the treewidth and degree; and that each problem in ECC (or CECC) is solvable in polynomial (O(nc)) time, when re stricted to graphs with a fixed upperbound on the treewidth (with given corresponding treedecomposition). Also, problems in CLCC and CECC are solvable in polynomial time for graphs with a logarithmic treewidth, and given corresponding treedecomposition, and in the case of CLCCproblems, a fixed upperbound on the degree of the graph. Also, we show
Algorithms For Vertex Partitioning Problems On Partial kTrees
, 1997
"... In this paper, we consider a large class of vertex partitioning problems and apply to those the theory of algorithm design for problems restricted to partial ktrees. We carefully describe the details of algorithms and analyze their complexity in an attempt to make the algorithms feasible as solutio ..."
Abstract

Cited by 40 (3 self)
 Add to MetaCart
In this paper, we consider a large class of vertex partitioning problems and apply to those the theory of algorithm design for problems restricted to partial ktrees. We carefully describe the details of algorithms and analyze their complexity in an attempt to make the algorithms feasible as solutions for practical applications.
Performance and Reliability Analysis Using Directed Acyclic Graphs
 IEEE Trans. Software Eng
, 1987
"... AbstractA graphbased modeling technique has been developed for the stochastic analysis of systems containing concurrency. The basis of the technique is the use of directed acyclic graphs. These graphs represent eventprecedence networks where activities may occur serially, probabilistically, or co ..."
Abstract

Cited by 39 (5 self)
 Add to MetaCart
AbstractA graphbased modeling technique has been developed for the stochastic analysis of systems containing concurrency. The basis of the technique is the use of directed acyclic graphs. These graphs represent eventprecedence networks where activities may occur serially, probabilistically, or concurrently. When a set of activities occurs concurrently, the condition for the set of activities to complete is that a specified number of the activities must complete. This includes the special cases that one or all of the activities must complete. The cumulative distribution function associated with an activity is assumed to have exponential polynomial form. Further generality is obtained by allowing these distributions to have a mass at the origin and/or at infinity. The distribution function for the time taken to complete the entire graph is computed symbolically in the time parameter t. The technique allows two or more graphs to be combined hierarchically. Applications of the technique to the evaluation of concurrent program execution time and to the reliability analysis of faulttolerant systems are discussed. Index TermsAvailability, directed acyclic graphs, faulttolerance, Markov models, performance evaluation, program performance, reliability. I.
The Steiner tree polytope and related polyhedra
, 1994
"... We consider the vertexweighted version of the undirected Steiner tree problem. In this problem, a cost is incurred both for the vertices and the edges present in the Steiner tree. We completely describe the associated polytope by linear inequalities when the underlying graph is seriesparallel. For ..."
Abstract

Cited by 27 (1 self)
 Add to MetaCart
We consider the vertexweighted version of the undirected Steiner tree problem. In this problem, a cost is incurred both for the vertices and the edges present in the Steiner tree. We completely describe the associated polytope by linear inequalities when the underlying graph is seriesparallel. For general graphs, this formulation can be interpreted as a (partial) extended formulation for the Steiner tree problem. By projecting this formulation, we obtain some very large classes of facetdefining valid inequalities for the Steiner tree polytope.
Combinatorial Optimization on Graphs of Bounded Treewidth
, 2007
"... There are many graph problems that can be solved in linear or polynomial time with a dynamic programming algorithm when the input graph has bounded treewidth. For combinatorial optimization problems, this is a useful approach for obtaining fixedparameter tractable algorithms. Starting from trees an ..."
Abstract

Cited by 21 (1 self)
 Add to MetaCart
There are many graph problems that can be solved in linear or polynomial time with a dynamic programming algorithm when the input graph has bounded treewidth. For combinatorial optimization problems, this is a useful approach for obtaining fixedparameter tractable algorithms. Starting from trees and seriesparallel graphs, we introduce the concepts of treewidth and tree decompositions, and illustrate the technique with the Weighted Independent Set problem as an example. The paper surveys some of the latest developments, putting an emphasis on applicability, on algorithms that exploit tree decompositions, and on algorithms that determine or approximate treewidth and find tree decompositions with optimal or close to optimal treewidth. Directions for further research and suggestions for further reading are also given.
Perfect Dominating Sets
, 1990
"... A dominating set S of a graph G is perfect if each vertex of G is dominated by exactly one vertex in S. We study the existence and construction of PDSs in families of graphs arising from the interconnection networks of parallel computers. These include trees, dags, seriesparallel graphs, meshes, to ..."
Abstract

Cited by 18 (2 self)
 Add to MetaCart
A dominating set S of a graph G is perfect if each vertex of G is dominated by exactly one vertex in S. We study the existence and construction of PDSs in families of graphs arising from the interconnection networks of parallel computers. These include trees, dags, seriesparallel graphs, meshes, tori, hypercubes, cubeconnected cycles, cubeconnected paths, and de Bruijn graphs. For trees, dags, and seriesparallel graphs we give linear time algorithms that determine if a PDS exists, and generate a PDS when one does. For 2 and 3dimensional meshes, 2dimensional tori, hypercubes, and cubeconnected paths we completely characterize which graphs have a PDS, and the structure of all PDSs. For higher dimensional meshes and tori, cubeconnected cycles, and de Bruijn graphs, we show the existence of a PDS in infinitely many cases, but our characterization is not complete. Our results include distance ddomination for arbitrary d. 1 Introduction Suppose G = (V; E) is a graph with vertex se...