TY - JOUR
T1 - Satisfiability problems on intervals and unit intervals
AU - Pe'er, Itsik
AU - Shamir, Ron
N1 - Funding Information:
* Portions of this paper were presented at the Third European Symposium on Algorithms, Corfu, Greece, 1996 [38]. * Corresponding author. E-mail: [email protected]. ’ Research supported in part by a grant from the Ministry of Science and the Arts, Israel.
PY - 1997/4/10
Y1 - 1997/4/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0346046160&partnerID=8YFLogxK
U2 - 10.1016/S0304-3975(96)00208-3
DO - 10.1016/S0304-3975(96)00208-3
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AN - SCOPUS:0346046160
SN - 0304-3975
VL - 175
SP - 349
EP - 372
JO - Theoretical Computer Science
JF - Theoretical Computer Science
IS - 2
ER -