Parallel Algorithms for Maximum Matching in Complements of Interval Graphs and Related Problems |
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Authors: | M G Andrews M J Atallah D Z Chen D T Lee |
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Affiliation: | (1) AT&T Bell Laboratories, 2000 N. Naperville Road, Naperville, IL 60566, USA. m.g.andrews@att.com., US;(2) Department of Computer Sciences, Purdue University, West Lafayette, IN 47907, USA. mja@cs.purdue.edu., US;(3) Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, USA. chen@cse.nd.edu., US;(4) Institute of Information Science, Academia Sinica, Nankang, Taiwan 11529. dtlee@iis.sinica.edu.tw., TW |
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Abstract: | Given a set of n intervals representing an interval graph, the problem of finding a maximum matching between pairs of disjoint (nonintersecting)
intervals has been considered in the sequential model. In this paper we present parallel algorithms for computing maximum
cardinality matchings among pairs of disjoint intervals in interval graphs in the EREW PRAM and hypercube models. For the
general case of the problem, our algorithms compute a maximum matching in O( log
3
n) time using O(n/ log
2
n) processors on the EREW PRAM and using n processors on the hypercubes. For the case of proper interval graphs, our algorithm runs in O( log n ) time using O(n) processors if the input intervals are not given already sorted and using O(n/ log n ) processors otherwise, on the EREW PRAM. On n -processor hypercubes, our algorithm for the proper interval case takes O( log n log log n ) time for unsorted input and O( log n ) time for sorted input. Our parallel results also lead to optimal sequential algorithms for computing maximum matchings
among disjoint intervals. In addition, we present an improved parallel algorithm for maximum matching between overlapping
intervals in proper interval graphs.
Received November 20, 1995; revised September 3, 1998. |
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Keywords: | , Parallel algorithms, Maximum matching problems, Interval graphs, Complement graphs, EREW PRAM, Hypercubes, |
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