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Durham University

Computer Science


Publication details for Dr George Mertzios

Mertzios, G.B., Nichterlein, A. & Niedermeier, R. (2018). A linear-time algorithm for maximum-cardinality matching on cocomparability graphs. SIAM Journal on Discrete Mathematics 32(4): 2820-2835.

Author(s) from Durham


Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph problems. For general $m$-edge and $n$-vertex graphs, it is well known to be solvable in $O(m\sqrt{n})$ time. We present a linear-time algorithm to find maximum-cardinality matchings on cocomparability graphs, a prominent subclass of perfect graphs that strictly contains interval graphs as well as permutation graphs. Our greedy algorithm is based on the recently discovered Lexicographic Depth First Search (LDFS).