TY - GEN

T1 - Feedback vertex set inspired kernel for chordal vertex deletion

AU - Agrawal, Akanksha

AU - Lokshtanov, Daniel

AU - Misra, Pranabendu

AU - Saurabh, Saket

AU - Zehavik, Meirav

N1 - Publisher Copyright:
Copyright © by SIAM.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Given a graph G and a parameter k, the Chordal Vertex Deletion (CVD) problem asks whether there exists a subset U V (G) of size at most k that hits all induced cycles of size at least 4. The existence of a polynomial kernel for CVD was a well-known open problem in the field of Parameterized Complexity. Recently, Jansen and Pilipczuk resolved this question affirmatively by designing a polynomial kernel for CVD of size O(k161 log58 k), and asked whether one can design a kernel of size O(k10). While we do not completely re- solve this question, we design a significantly smaller kernel of size O(k25 log14 k), inspired by the O(k2)-size kernel for Feedback Vertex Set. To obtain this result, we first design an O(optlog2 n)-factor approximation al- gorithm for CVD, which is central to our kernelization procedure. Thus, we improve upon both the kernel- ization algorithm and the approximation algorithm of Jansen and Pilipczuk. Next, we introduce the notion of the independence degree of a vertex, which is our main conceptual contribution. We believe that this notion could be useful in designing kernels for other problems.

AB - Given a graph G and a parameter k, the Chordal Vertex Deletion (CVD) problem asks whether there exists a subset U V (G) of size at most k that hits all induced cycles of size at least 4. The existence of a polynomial kernel for CVD was a well-known open problem in the field of Parameterized Complexity. Recently, Jansen and Pilipczuk resolved this question affirmatively by designing a polynomial kernel for CVD of size O(k161 log58 k), and asked whether one can design a kernel of size O(k10). While we do not completely re- solve this question, we design a significantly smaller kernel of size O(k25 log14 k), inspired by the O(k2)-size kernel for Feedback Vertex Set. To obtain this result, we first design an O(optlog2 n)-factor approximation al- gorithm for CVD, which is central to our kernelization procedure. Thus, we improve upon both the kernel- ization algorithm and the approximation algorithm of Jansen and Pilipczuk. Next, we introduce the notion of the independence degree of a vertex, which is our main conceptual contribution. We believe that this notion could be useful in designing kernels for other problems.

UR - http://www.scopus.com/inward/record.url?scp=85016209705&partnerID=8YFLogxK

U2 - 10.1137/1.9781611974782.90

DO - 10.1137/1.9781611974782.90

M3 - Conference contribution

AN - SCOPUS:85016209705

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1383

EP - 1398

BT - 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017

A2 - Klein, Philip N.

PB - Association for Computing Machinery

T2 - 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017

Y2 - 16 January 2017 through 19 January 2017

ER -