Approximating Multistage Matching Problems

Abstract In multistage perfect matching problems, we are given a sequence of graphs on the same vertex set and asked to find matchings, corresponding graphs, such that consecutive matchings as similar possible. More precisely, aim maximize intersections, or minimize unions between matchings. We show these problems NP-hard even in very restricted scenarios. As our main contribution, present first non-trivial approximation algorithms for problems: On one hand, devise tight graph sequences length two (2-stage graphs). other propose several general methods deduce approximations from blackbox 2-stage graphs.