TY - GEN
T1 - Optimization problems in dotted interval graphs
AU - Hermelin, Danny
AU - Mestre, Julián
AU - Rawitz, Dror
PY - 2012
Y1 - 2012
N2 - The class of D-dotted interval (D-DI) graphs is the class of intersection graphs of arithmetic progressions with jump (common difference) at most D. We consider various classical graph-theoretic optimization problems in D-DI graphs of arbitrarily, but fixed, D. We show that Maximum Independent Set, Minimum Vertex Cover, and Minimum Dominating Set can be solved in polynomial time in this graph class, answering an open question posed by Jiang (Inf. Processing Letters, 98(1):29-33, 2006). We also show that Minimum Vertex Cover can be approximated within a factor of (1∈+∈ε) for any ε∈>∈0 in linear time. This algorithm generalizes to a wide class of deletion problems including the classical Minimum Feedback Vertex Set and Minimum Planar Deletion problems. Our algorithms are based on classical results in algorithmic graph theory and new structural properties of D-DI graphs that may be of independent interest.
AB - The class of D-dotted interval (D-DI) graphs is the class of intersection graphs of arithmetic progressions with jump (common difference) at most D. We consider various classical graph-theoretic optimization problems in D-DI graphs of arbitrarily, but fixed, D. We show that Maximum Independent Set, Minimum Vertex Cover, and Minimum Dominating Set can be solved in polynomial time in this graph class, answering an open question posed by Jiang (Inf. Processing Letters, 98(1):29-33, 2006). We also show that Minimum Vertex Cover can be approximated within a factor of (1∈+∈ε) for any ε∈>∈0 in linear time. This algorithm generalizes to a wide class of deletion problems including the classical Minimum Feedback Vertex Set and Minimum Planar Deletion problems. Our algorithms are based on classical results in algorithmic graph theory and new structural properties of D-DI graphs that may be of independent interest.
UR - http://www.scopus.com/inward/record.url?scp=84868009908&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-34611-8_8
DO - 10.1007/978-3-642-34611-8_8
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AN - SCOPUS:84868009908
SN - 9783642346101
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 46
EP - 56
BT - Graph-Theoretic Concepts in Computer Science - 38th International Workshop, WG 2012, Revised Selcted Papers
T2 - 38th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2012
Y2 - 26 June 2012 through 28 June 2012
ER -