Kenji Onaga

Legal firing sequence and related problems of Petri nets

Development of computational tools and techniques dealing with large-scale Petri nets will provide a firm foundation of Petri net theory. A discussion is presented of the computational complexity aspect of the legal firing sequence problem (LFS) and some related problems of Petri nets, each having applications to practical problems. Their NP-completeness and polynomial-time solvability are presented.<<ETX>>

Genetic algorithm for sex-fair stable marriage problem

In this paper we consider a sex-fair matching in the stable marriage problem. The sex-fair stable matching defined in this paper has a property that the sum of the partners rank of each man in his preference list is as close as possible to the sum of the partners rank of each woman in her preference list. We transform the sex-fair marriage problem into a graph problem which is suitable for a genetic algorithm. We propose a genetic algorithm for the sex-fair stable matching. The transformation into the graph problem makes application of the GA easier and effective. Computer experiments show the effectiveness of the proposed genetic algorithm.

A wavefront algorithm for LU decomposition of a partitioned matrix on VLSI processor

For distributed-memory multicomputers such as the Intel Paragon, the IBM SP-1/SP-2, the NCUBE/2, and the Thinking Machines CM-5, the quality of the data partitioning for a given application is crucial to obtaining high performace. This task has traditionally been the users responsibility, but in recent years much effort has been directed to automating the selection of data partitioning schemes. Several researchers have proposed systems that are able to produce data distributons that remain in effect for the entire execution of an application. For complex programs, however, such static data distributions may be insufficient to obtain acceptable performance. The selection of distributions that dynamically change over the course of a programs execution adds another dimension to the data partitioning problem. In this paper, we present a technique that can be used to automatically determine which partitionings are most beneficial over specific sections of a program while taking into account the added overhead of performing redistribution. This system has been implemented as part of the PARADIGM (PARAllelizing compiler for DIstributed-memory General-purpose Multicomputers) project at the University of Illinois. The complete system strives to provide a fully automated means to parallelize programs written in a serial programming model obtaining high performance on a wide range of distributed-memory multicomputers.

Execution termination and computation determinacy of data-flow program nets

Abstract This paper deals with execution termination and computation determinacy of data-flow program nets, which are extended from conventional data-flow program graphs by allowing edge thresholds α and β to be any positive integer number, while a conventional data-flow graph has α = β = 1. First detailed description of program nets is presented and then the problems of execution termination and computation determinacy of a given data-flow program net are analysed. Through structural analysis of net activities, the following results are obtained in this paper: (1) necessary and sufficient conditions for any execution of a switchless net to terminate; (2) sufficient conditions for any execution of a program net, including SWITCH-nodes, to terminate; and (3) sufficient conditions of computation determinacy.

Vertex covers and connected vertex covers in 3-connected graphs

Discusses time complexity analysis of the minimum vertex cover and minimum connected vertex cover problems for 3-connected graphs. A vertex cover of a graph G=(V, E) is a subset N of V such that each element of E is incident upon some element of N, where V and E are the sets of vertices and of edges of G, respectively. A connected vertex cover of a graph G is a vertex cover of G such that the subgraph G(N) induced by N of G is connected. The minimum vertex cover problem (VCP) is the problem of finding a vertex cover of minimum cardinality, and the minimum connected vertex cover problem is similarly defined.<<ETX>>

Legal firing sequences and minimum initial markings for Petri nets

Computational complexity and approximation algorithms for the legal firing sequence (LFS) and minimum initial marking (MIM) problem for a Petri net PN are discussed. The NP-completeness of LFS for a consistent free-choice net PN with an elementary T-invariant is proved, and an algorithm for LFS with PN restricted to a persistent Petri net is given. It is also shown that MIM is NP-complete even if PN is a weakly connected marked graph with each node having a total in-degree and out-degree of at most three. Some approximation algorithms for MIM are proposed.<<ETX>>

Finding jumpers in printed wiring board design for analog circuits

Reducing the number of jumpers is one of the most critical problems in the design of single-layered printed wiring boards for analog circuits. An O ( mod V//E mod ) algorithm is proposed for finding a small set of jumpers. Evaluation is also given through experimental results on practical analog circuits.<<ETX>>

A parallel tabu search and its hybridization with genetic algorithms

The paper proposes two parallel meta-heuristics. One is a cooperative parallel tabu search which incorporates historical information exchange among processors in addition to its own searching of each processor. The other is a cooperative parallel search between genetic algorithm and tabu search processes. Through computational experiment, we observe the improvement of solutions by our proposed method.

A polynomial-time algorithm for finding a semi-generator of Petri net invariants

A polynomial-time algorithm is proposed for finding a semigenerator of Petri net invariants. Invariants of a Petri net are solutions to a linear system of equations Ax=0 for the place-transition incidence matrix A representing this Petri net. The notion of a semigenerator is introduced: it is a maximal subset consisting of linearly independent elements of a generator, and any invariant can be expressed as linear combination of those elements in the set with negative coefficients allowed. The proposed algorithm adopts a linear programming technique.<<ETX>>

A congestion-cost-directed router for VLSI switchboxes

A switchbox router called CONDOR that is directed by predictive and corrective congestion cost is proposed. The distinctions of CONDOR are twofold: the first is incorporation of path reshaping in the computation of congestion costs, and the second is separation of the routing algorithm from the constraints and characteristics of switchbox layout. It is stressed that this separation increases applicability of the algorithm to other routing problems by using graph models to address conditions specific to those problems.<<ETX>>