A fast algorithm for minimum weight odd cuts and circuits in planar graphs

Letchford, A N and Pearson, N (2005) A fast algorithm for minimum weight odd cuts and circuits in planar graphs. Operations Research Letters, 33 (6). pp. 625-628. ISSN 0167-6377

Abstract

We give a simple O(n^{3/2} log n) algorithm for finding a minimum weight odd circuit in planar graphs. By geometric duality, the same algorithm can be used to find minimum weight odd cuts. For general sparse graphs, the fastest known algorithms for these two problems take O(n^2 log n) time and O(n^3 log n) time, respectively.