Polynomial kernels for Proper Interval Completion and related problems

Given a graph G=(V,E) and a positive integer k, the Proper Interval Completion problem asks whether there exists a set F of at most k pairs of (V×V)∖E such that the graph H=(V,E∪F) is a proper interval graph. The Proper Interval Completion problem finds applications in molecular biology and genomic...

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Bibliographic Details
Published in:Information and computation Vol. 231; pp. 89 - 108
Main Authors: Bessy, Stéphane, Perez, Anthony
Format: Journal Article
Language:English
Published: Elsevier Inc 01.10.2013
Elsevier
Subjects:
Computer Science
Data Structures and Algorithms
Graph modification problems
Kernelization algorithms
Parameterized complexity
Proper interval graphs
Graph modification problems
Proper interval graphs
Kernelization algorithms
Parameterized complexity
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:Given a graph G=(V,E) and a positive integer k, the Proper Interval Completion problem asks whether there exists a set F of at most k pairs of (V×V)∖E such that the graph H=(V,E∪F) is a proper interval graph. The Proper Interval Completion problem finds applications in molecular biology and genomic research. This problem is known to be FPT (Kaplan, Tarjan and Shamir, FOCSʼ94), but no polynomial kernel was known to exist. We settle this question by proving that Proper Interval Completion admits a kernel with O(k3) vertices. Moreover, we prove that a related problem, the so-called Bipartite Chain Deletion problem, admits a kernel with O(k2) vertices, completing a previous result of Guo (ISAACʼ07).
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2013.08.006