Narsingh Deo

Shortest‐path algorithms: Taxonomy and annotation

We have evolved a classification scheme to characterize algorithms for solving shortestpath problems. The algorithms are classified according to (A) the problem type, i.e., the question being asked about the given network; (B) the input type, i.e., the salient features of the given network which impact on the design of the algorithm and selection of data structures; and (C) the type of underlying technique employed to solve the problem. An annotated bibliography of 79 selected references on shortest-path algorithms is included. We have also provided a more complete listing of 222 references carefully culled out of a larger body of literature on shortest-path algorithms through the year 1979.

On Algorithms for Enumerating All Circuits of a Graph

A brief description and comparison of all known algorithms for enumerating all circuits of a graph is provided, and upper bounds on computation time of many algorithms are derived. The vector space...

Parallel graph algorithms

Algorithms and data structures developed to solve graph problems on parallel computers are surveyed. The problems discussed relate to searching graphs and finding connected components, maximal chques, maximum cardinahty matchings, mimmum spanning trees, shortest paths, and travehng salesman tours. The algorithms are based on a number of models of parallel computation, including systohc arrays, assoclatwe processors, array processors, and mulhple CPU computers. The most popular model is a direct extension of the standard RAM model of sequential computation. It may not, however, be the best basis for the study of parallel algorithms. More emphasis has been focused recently on communications issues in the analysis of the complexity of parallel algorithms; thus parallel models are coming to be more complementary to implementable architectures. Most algorithms use relatwely simple data structures, such as the adjacency matrix and adjacency hsts, although a few algorithms using linked hsts, heaps, and trees are also discussed.

A comparison of algorithms for terminal-pair reliability

Four algorithms for the terminal-pair-reliability problem are compared. Nelson (1970), Lin (1976), Shooman (1968), and Dotson (1979) algorithms are used in this study. It is shown that the Dotson algorithm is the fastest among the terminal-pair reliability algorithms analyzed. The Dotson algorithm is suited not only for numerical reliability, but for obtaining symbolic expression for the terminal-pair reliability with no additional effort. By modifying the Dotson algorithm the efficiency can be further improved. The modifications to this algorithm are listed and the reliability of the modified Dotson algorithm is computed. >

Exact and Approximate Solutions for the Gate Matrix Layout Problem

We consider the gate matrix layout problem for VLSI circuits, which is known to be NP-complete. We present an efficient algorithm for determining whether two tracks suffice. For the general problem of minimizing the number of tracks (and, hence, the area) needed, we design an attractive dynamic programming formulation to guarantee optimality. We also investigate the performance of fast heuristic algorithms published in the literature and demonstrate that there exist families of problem instances for which the ratio of the number of tracks required by these heuristics to the optimal value is unbounded. Moreover, we show that this result holds for any on-line layout algorithm. We additionally prove that, unless P = NP, no polynomial-time layout algorithm can ensure that the number of tracks it requires never exceeds k plus the optimum, for any constant k.

Node-Deletion NP-Complete Problems

The entire class of node-deletion problems can be stated as follows: Given a graph G, find the minimum number of nodes to be deleted so that the remaining subgraph g satisfies a specified property

Parallel heap: an optimal parallel priority queue

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Minimum-weight degree-constrained spanning tree problem: heuristics and implementation on an SIMD parallel machine

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Random-tree diameter and the diameter-constrained MST

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Computing a Diameter-Constrained Minimum Spanning Tree in Parallel

, a distinct node-deletion problem arises. The various deletion problems considered here are for the following properties: each component of g is (i) null, (ii) complete, (iii) a tree, (iv) nonseparable, (v) planar, (vi) acyclic, (vii) bipartite, (viii) transitive, (ix) Hamiltonian, (x) outerplanar, (xi) degree-constrained, (xii) line invertible, (xiii) without cycles of a specified length, (xiv) with a singleton K-basis, (xv) transitively orientable, (xvi) chordal, and (xvii) interval. In this paper, these 17 different node-deletion problems are shown to be NP-complete. A unified approach is taken for the transformations employed in the proofs.