Compression via matroids: a randomized polynomial kernel for odd cycle transversal

The Odd Cycle Transversal problem (OCT) asks whether a given graph can be made bipartite by deleting at most k of its vertices. In a breakthrough result Reed, Smith, and Vetta (Operations Research Letters, 2004) gave a O(4k kmn) time algorithm for it, the first algorithm with polynomial runtime of uniform degree for every fixed k. It is known that this implies a polynomial-time compression algorithm that turns OCT instances into equivalent instances of size at most O(4k ), a so-called kernelization. Since then the existence of a polynomial kernel for OCT, i.e., a kernelization with size bounded polynomially in k, has turned into one of the main open questions in the study of kernelization. Despite the impressive progress in the area, including the recent development of lower bound techniques (Bodlaender et al., ICALP 2008; Fortnow and Santhanam, STOC 2008) and meta-results on kernelizations for graph problems on planar and other sparse graph classes (Bodlaender et al., FOCS 2009; Fo...

• Type: Journal
• Year: 2012
• Where: SODA
• Authors: Stefan Kratsch, Magnus Wahlström
• Keywords: Algorithms, Operations Research Letters, SODA 2012, Sparse Graph Classes, STOC 2005