Contribution
Satisfiability problems on intervals and unit intervals

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Abstract

For an interval graph with some additional order constraints between pairs of non-intersecting intervals, we give a linear time algorithm to determine if there exists a realization which respects the order constraints. Previous algorithms for this problem (known also as seriation with side constraints) required quadratic time. This problem contains as subproblems interval graph and interval order recognition. On the other hand, it is a special case of the interval satisfiability problem, which is concerned with the realizability of a set of intervals along a line, subject to precedence and intersection constraints. We study such problems for all possible restrictions on the types of constraints, when all intervals must have the same length. We give efficient algorithms for several restrictions of the problem, and show the NP-completeness of another restriction.

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Portions of this paper were presented at the Third European Symposium on Algorithms, Corfu, Greece, 1996 [38].

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Research supported in part by a grant from the Ministry of Science and the Arts, Israel.