205875710
A proof of a conjecture of minus domination in graphs
Let γ-(G) be the minus domination number of a graph G. It has been conjectured in Discrete Math. 199 (1999) 35 that γ-(G) ≥ 4((1 + n)1/2 - 1) - n for all bipartite graph of order n. In this paper we prove this conjecture.
46728752
Some more remarks on domination in cubic graphs
Abstract We give sharp upper bounds on the upper signed domination number of nearly regular graphs and on the minus domination number of connected cubic graphs.
31866645
Optimal Processor Mapping for Linear-Complement Communication on Hypercubes
In this paper, we address the problem of minimizing channel contention of linear-complement communication on wormhole-routed hypercubes. Our research reveals that, for traditional routing algorithms, the degree of channel contention of a linear-complement communication can be quite large. To solve this problem, we propose an alternative approach, which applies processor reordering mapping at compile time. In this compiler approach, processors are logically reordered according to the given communication(s) so that the new communication(s) can be efficiently realized on the hypercube network. It is proved that, for any linear-complement communication, there exists a reordering mapping such that the new communication has minimum channel contention. An O(n/sup 3/) algorithm is proposed to find such a mapping for an n-dimensional hypercube. An algorithm based on dynamic programming is also proposed to find an optimal reordering mapping for a set of linear-complement communications. Several computer simulations have been conducted and the results clearly show the advantage of the proposed approach.
7877505
Three forbidden subgraphs for line graphs
We construct a set of three graphs with the property that a 3-connected graph with minimum degree at least 7 is a line graph if and only if it does not contain any of the three graphs as an induced subgraph. We also show that the number of excluded subgraphs cannot be reduced no matter what connectivity is specified.
6254649
Disjunctive Image Computation for Embedded Software Verification
Finite state models generated from software programs have unique characteristics that are not exploited by existing model checking algorithms. In this paper, we propose a novel disjunctive image computation algorithm and other simplifications based on these characteristics. Our algorithm divides an image computation into a disjunctive set of easier ones that can be performed in isolation. Hypergraph partitioning is used to minimize the number of live variables in each disjunctive component. We use the live variables to simplify transition relations and reachable state subsets. Our experiments on a set of real-world C programs show that the new algorithm achieves orders-of-magnitude performance improvement over the best known conjunctive image computation algorithm
18478446
On Parallel Complexity of Planar Triangulations
The greedy triangulation of a finite planar point set is obtained by repeatedly inserting a shortest diagonal that doesn't intersect those already in the plane. We show that the problem of constructing the greedy triangulation of a finite set of points with integer coordinates in the plane is P-complete. This is the first known geometric P-complete problem where the input is given as a set of points. On the other hand, we provide general NC-methods for testing whether a given triangulation of a set of points and/or line segments can be built by inserting the diagonals in a given partial order, and for constructing such triangulations for simple polygons. As corollaries, we obtain NC-algorithms for testing whether a triangulation is respectively the greedy triangulation or the so called sweep-line triangulation, and for constructing respectively the greedy triangulation or the sweep-line triangulation of a simple polygon. The latter result solves the open problem posed by Atallah et al.
10710066
An Algorithm for the Chromatic Number of a Graph
Christofides' algorithm for finding the chromatic number of a graph is improved both in speed and memory space by using a depth-first search rule to search for a shortest path in a reduced subgraph tree.