A projective plane is equivalent to a disk with antipodal points identified. A graph is projective planar if it can be drawn on the projective plane with no crossing edges. A linear time algorithm for projective plana...
详细信息
We consider the general problem of determining a smallest set of edges which must be added to a given graph (hyper graph, digraph)in order to make it k-edge-connected (k-vertex-connected). We give a short summary of t...
详细信息
Treewidth is a graph measure with several applications. In this abstract, it is discussed that many otherwise intractable problems become polynomial or linear time solvable when restricted to graphs of bounded treewid...
详细信息
Treewidth is a graph measure with several applications. In this abstract, it is discussed that many otherwise intractable problems become polynomial or linear time solvable when restricted to graphs of bounded treewidth, and some other algorithmic results that use treewidth (e.g., applied to planar graphs) are discussed.
We address a practical problem which arises in several areas, including network design and VLSI circuit layout. Given an undirected weighted graph G = ( V , E and a family N = [ N 1 , …, N k ] of k disjoint groups of...
详细信息
In this paper we consider an optimal vertex ordering problem of graphs. The vertex ordering and an optimality measure are defined. It is proved that the optimal ordering problem under consideration can be transformed ...
详细信息
In this paper we consider an optimal vertex ordering problem of graphs. The vertex ordering and an optimality measure are defined. It is proved that the optimal ordering problem under consideration can be transformed into the well-known minimum-weight spanning tree problem and is therefore solvable in low-polynomial time. We also investigate some properties of optimal vertex orderings. (C) 1999 Elsevier Science B.V. All rights reserved.
We present fast and efficient parallel algorithms for finding the connected components of an undirected graph. These algorithms run on the exclusive-read, exclusive-write (EREW) PRAM. On a graph with n vertices and m ...
详细信息
We present fast and efficient parallel algorithms for finding the connected components of an undirected graph. These algorithms run on the exclusive-read, exclusive-write (EREW) PRAM. On a graph with n vertices and m edges, our randomized algorithm runs in O(log n) time using (m + n(1+epsilon)) = log n EREW processors (for any fixed epsilon > 0). A variant uses (m + n)= log n processors and runs in O(log n log log n) time. A deterministic version of the algorithm runs in O(log(1.5) n) time using m + n EREW processors.
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 clas...
详细信息
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 + epsilon) of exactly in half.
Local search with k-change neighborhoods is perhaps the oldest and most widely used heuristic method for the traveling salesman problem, yet almost no theoretical performance guarantees for it were previously known. T...
详细信息
Local search with k-change neighborhoods is perhaps the oldest and most widely used heuristic method for the traveling salesman problem, yet almost no theoretical performance guarantees for it were previously known. This paper develops several results, some worst-case and some probabilistic, on the performance of 2- and k-opt local search for the traveling salesman problem, with respect to both the quality of the solution and the speed with which it is obtained.
Given a graph G and a vertex nu, a vertex u is an element of N(nu) is a maximum neighbor of nu if for all w is an element of N(nu) we have N(zu) subset of or equal to N(u), where N(nu) denotes the neighborhood of nu i...
详细信息
Given a graph G and a vertex nu, a vertex u is an element of N(nu) is a maximum neighbor of nu if for all w is an element of N(nu) we have N(zu) subset of or equal to N(u), where N(nu) denotes the neighborhood of nu in G. A maximum neighborhood elimination order of G is a linear order nu(1), nu(2),..., nu(n) on its vertex set such that there is a maximum neighbor of v(i) in the subgraph G[v(1),..., v(i)]. A graph is dually chordal if it admits a maximum neighborhood elimination order. Alternatively, a graph is dually chordal if it is the clique graph of a chordal graph. The class of dually chordal graphs generalizes known subclasses of chordal graphs such as doubly chordal graphs, strongly chordal graphs, interval graphs, and indifference graphs. We prove that Vizing's total-color conjecture holds for dually chordal graphs. We describe a new heuristic that Fields an exact total coloring for even maximum degree dually chordal graphs and an exact edge coloring for odd maximum degree dually chordal graphs. (C) 1999 Elsevier Science B.V. All rights reserved.
Stack layouts and queue layouts of undirected graphs have been used to model problems in fault tolerant computing and in parallel process scheduling. However, problems in parallel process scheduling are more accuratel...
详细信息
Stack layouts and queue layouts of undirected graphs have been used to model problems in fault tolerant computing and in parallel process scheduling. However, problems in parallel process scheduling are more accurately modeled by stack and queue layouts of directed acyclic graphs (dags). A stack layout of a dag is similar to a stack layout of an undirected graph, with the additional requirement that the nodes of the dag be in some topological order. A queue layout is defined in an analogous manner. The stacknumber (queuenumber) of a dag is the smallest number of stacks (queues) required for its stack layout (queue layout). This paper presents algorithmic results-in particular, linear time algorithms for recognizing 1-stack dags and 1-queue dags, and proofs of NP-completeness for the problem of recognizing a 4-queue dag and the problem of recognizing a 6-stack dag. The companion paper (Part I [SIAM J. Comput., 28 (1999), pp. 1510-1539.]) presents combinatorial results.
暂无评论