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1973

Volume 2, Issue 4, pp. 217-318


Toward Characterization of Perfect Elimination Digraphs

Loren Haskins and Donald J. Rose

SIAM J. Comput. 2, pp. 217-224 (8 pages) | Cited 5 times

Online Publication Date: July 13, 2006

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Perfect elimination digraphs arise in the study of Gaussian elimination on sparse linear systems. With a view toward numerical computational complexity we show four conditions (C1–C4) to be necessary for the perfect elimination property. The sufficiency of C1 is shown in general and the sufficiency of C2–C4 is shown in the symmetric case. The equivalence of C1–C3 is conjectured.

An $n^{5/2} $ Algorithm for Maximum Matchings in Bipartite Graphs

John E. Hopcroft and Richard M. Karp

SIAM J. Comput. 2, pp. 225-231 (7 pages) | Cited 101 times

Online Publication Date: July 13, 2006

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The present paper shows how to construct a maximum matching in a bipartite graph with $n$ vertices and $m$ edges in a number of computation steps proportional to $(m + n)\sqrt n $.

Queueing Analysis of a Multiprogrammed Computer System Having a Multilevel Storage Hierarchy

Stephen S. Lavenberg

SIAM J. Comput. 2, pp. 232-252 (21 pages) | Cited 2 times

Online Publication Date: July 13, 2006

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We formulate a class of closed queueing network models which can be used to represent certain features of multiprogrammed computer systems having multilevel storage hierarchies. The resources which comprise the system are described by a network of interconnected multiserver stages where each stage can provide more than one type of service. The sequence of services required by a program executing in the system is described by a finite Markov chain over the service types. This description permits an explicit representation in the model of the data transfers which occur as determined by the data transfer rules and data paths in the hierarchy. The queueing discipline at each stage is nonpreemptive priority among the types of service provided by the stage, and first-come first-served within a service type.
We derive simple expressions relating the work rates for different stages and obtain simple upper bounds on the work rates. These results are valid for general service time distributions. We then apply a model in this class to the analysis of a multiprogrammed three level staging hierarchy. Under the assumption that all service time distributions are exponential, we numerically investigate the effects on system performance of different service priorities and of varying the program load parameters and level of multiprogramming.

Continuous Group Averaging and Pattern Classification Problems

J. C. Dunn

SIAM J. Comput. 2, pp. 253-272 (20 pages) | Cited 1 time

Online Publication Date: July 13, 2006

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The relationship between pattern classification problems and the elementary theory of group invariants is considered. A general procedure for obtaining quantitative invariants by averaging functionals over the manifold of a continuous group is examined in some detail, and then applied to the classification of plane figures. Specifically, the Fourier transform of a plane figure is averaged over the one-parameter continuous group of dilatations to obtain a pair of interesting scale invariant transforms which tend to pick out corners and flat spots in the figure’s boundary.

On Optimal Processor Scheduling for Multiprogramming

L. J. Bass

SIAM J. Comput. 2, pp. 273-280 (8 pages)

Online Publication Date: July 13, 2006

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This paper investigates the problem of scheduling a processor to optimize throughput in a multiprogramming environment. A deterministic model is used to study the scheduling of a batch of $k$ programs residing in main memory of a system consisting of a single processor and $k$ input–output devices in such a way as to minimize the time to complete all $k$ jobs.
It is shown that for any set of independent programs a preemptive strategy is not necessary to obtain the minimum running time for the entire batch. There is always an interrupt driven schedule which is as good as the best preemptive schedule.
It is also shown that processor bound programs are easy to schedule. A lower bound on the completion time for any set of programs is observed, and it is shown that with processor bound programs the lower bound can always be obtained. An algorithm for obtaining this bound is given.
These results provide some insight into the workings of the dynamic scheduling algorithms in use in many modern computer systems.

An Algorithm for the Extreme Rays of a Pointed Convex Polyhedral Cone

Walter B. McRae and Ernest R. Davidson

SIAM J. Comput. 2, pp. 281-293 (13 pages) | Cited 4 times

Online Publication Date: July 13, 2006

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An algorithm for exhibiting the extreme rays of a pointed convex polyhedral cone is described. The cone is assumed to be initially defined by a system of homogeneous linear inequalities. The method differs from prior procedures in two respects. First, faces of lower dimension than facets for the polar convex cone are used to serially determine the extreme rays; second, the method allows for the possibility of symmetry considerations involving the extreme rays to reduce storage requirements and computation effort.

Set Merging Algorithms

J. E. Hopcroft and J. D. Ullman

SIAM J. Comput. 2, pp. 294-303 (10 pages) | Cited 21 times

Online Publication Date: July 13, 2006

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This paper considers the problem of merging sets formed from a total of $n$ items in such a way that at any time, the name of a set containing a given item can be ascertained. Two algorithms using different data structures are discussed. The execution times of both algorithms are bounded by a constant times $nG(n)$, where $G(n)$ is a function whose asymptotic growth rate is less than that of any finite number of logarithms of $n$.

The Hardest Context-Free Language

Sheila A. Greibach

SIAM J. Comput. 2, pp. 304-310 (7 pages) | Cited 18 times

Online Publication Date: July 13, 2006

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There is a context-free language $L_0 $ such that every context-free language is an inverse homomorphic image of $L_0 $ or $L_0 - \{ e\} $. Hence the time complexity of recognition of $L_0 $ is the least upper bound for time complexity of recognition of context-free languages. A similar result holds for quasirealtime Turing machine languages. Several languages are given such that deterministic and nondeterministic polynomial time acceptance are equivalent if and only if any one of them is deterministic polynomial time acceptable.

An Algorithm for Determining the Chromatic Number of a Graph

D. G. Corneil and B. Graham

SIAM J. Comput. 2, pp. 311-318 (8 pages) | Cited 5 times

Online Publication Date: July 13, 2006

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A heuristic algorithm for the determination of the chromatic number of a finite graph is presented. This algorithm is based on Zykov’s theorem for chromatic polynomials, and extensive empirical tests show that it is the best algorithm available. Christofides’ algorithm for the determination of chromatic number is described and is used in the comparison tests.
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