PARALLEL MAXIMUM MATCHING ALGORITHMS IN INTERVAL GRAPHS

We develop efficient parallel maximum matching algorithms in interval graphs by exploiting special properties of interval graphs. For general interval graphs, our algorithm requires O( log 2v+(n log n/v) time and O(nv2+n2) operations on the CREW PRAM, where n is the number of intervals and v≤n is a parameter. By choosing [Formula: see text], we obtain an [Formula: see text]-time algorithm in O(n2) operations. For v=n/ log n, we have an O( log 2n)-time algorithm in O(n3/ log 2n) operations. The best previously known solution takes O( log 2n) time using O(n3 log 2n) operations. For proper interval graphs, our algorithm runs in O( log n) time using O(n) operations if input intervals are sorted and using O(n log n) operations otherwise on the EREW PRAM.