Ramjee P. Swaminathan

On finding solutions for extended Horn formulas

Abstract We present a simple quadratic-time algorithm for solving the satisfiability problem for a special class of boolean formulas. This class properly contains the class of extended Horn formulas and balanced formulas. Previous algorithms for these classes require testing membership in the classes. However, the problem of recognizing balanced formulas is complex, and the problem of recognizing extended Horn formulas is not known to be solvable in polynomial time. Our algorithm requires no such test for membership.

The arborescence-realization problem

A {0, 1}-matrix M is arborescence graphic if there exists an arborescence T such that the arcs of T are indexed on the rows of M and the columns of M are the incidence vectors of the arc sets of dipaths of T. If such a T exists, then T is an arborescence realization for M. This paper presents an almost-linear-time algorithm to determine whether a given {0, 1}-matrix is arborescence graphic and, if so, to construct an arborescence realization. The algorithm is then applied to recognize a subclass of the extended-Horn satisfiability problems introduced by Chandru and Hooker (1991).

The pagenumber of the class of bandwidth- k graphs is k −1

Abstract It is shown that a bandwidth-k graph can be embedded in k − 1 pages with respect to a linear ordering of its vertices and that there exists a set of bandwidth-k graphs that need k − 1 pages. In other words, the pagenumber of the class of bandwidth-k graphs is k − 1.

An algorithm for the class of pure implicational formulas

Abstract Heusch introduced the notion of pure implicational formulas. He showed that the falsifiability problem for pure implicational formulas with k negations is solvable in time O (n k ) . Such falsifiability results are easily transformed to satisfiability results on CNF formulas. We show that the falsifiability problem for pure implicational formulas is solvable in time O (k k n 2 ) , which is polynomial for a fixed k. Thus this problem is fixed-parameter tractable.

On the Consecutive-Retrieval Problem

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Average case results for satisfiability algorithms under the random-clause-width model

\{0,1\}

A multi-tree routing scheme using acyclic orientations

-matrix

On good algorithms for determining unsatisfiability of propositional formulas

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A Multi-Tree Generating Routing Scheme Using Acyclic Orientations

has the consecutive-retrieval property if there exists a tree

On testing consecutive-ones property in parallel

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