Parallel maximum matching algorithms in interval graphs

We develop new parallel maximum matching algorithms in interval graphs by exploiting the characteristics of interval graphs. For general interval graphs, our algorithm requires O(log² v+(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 v=√n, we obtain an O(√n log n)-time algorithm in O(n²) operations. For v=n/log n, we have an O(log² n)-time algorithm with n³/log⁴ n processors. The previously best known solution takes O(log² n) time with n ³ processors. For proper interval graphs, our algorithm runs in O(log n) time using n/log n processors if input intervals are sorted and using n processors otherwise on the EREW PRAM. Our algorithms are much simpler than the previous ones