TY - GEN
T1 - Exploiting a hypergraph model for finding golomb rulers
AU - Sorge, Manuel
AU - Moser, Hannes
AU - Niedermeier, Rolf
AU - Weller, Mathias
PY - 2012/8/27
Y1 - 2012/8/27
N2 - Golomb rulers are special rulers where for any two marks it holds that the distance between them is unique. They find applications in positioning of radio channels, radio astronomy, communication networks, and bioinformatics. An important subproblem in constructing "compact" Golomb rulers is Golomb Subruler (GSR), which asks whether it is possible to make a given ruler Golomb by removing at most k marks. We initiate a study of GSR from a parameterized complexity perspective. In particular, we develop a hypergraph characterization of rulers and consider the construction and structure of the corresponding hypergraphs. We exploit their properties to derive polynomial-time data reduction rules that lead to a problem kernel for GSR with O(k 3) marks. Finally, we provide a simplified NP-hardness construction for GSR.
AB - Golomb rulers are special rulers where for any two marks it holds that the distance between them is unique. They find applications in positioning of radio channels, radio astronomy, communication networks, and bioinformatics. An important subproblem in constructing "compact" Golomb rulers is Golomb Subruler (GSR), which asks whether it is possible to make a given ruler Golomb by removing at most k marks. We initiate a study of GSR from a parameterized complexity perspective. In particular, we develop a hypergraph characterization of rulers and consider the construction and structure of the corresponding hypergraphs. We exploit their properties to derive polynomial-time data reduction rules that lead to a problem kernel for GSR with O(k 3) marks. Finally, we provide a simplified NP-hardness construction for GSR.
KW - Data Reduction
KW - Forbidden Subgraph Characterization
KW - Hitting Set
KW - NP-Hardness
KW - Parameterized Complexity
KW - Problem Kernel
UR - http://www.scopus.com/inward/record.url?scp=84865205367&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-32147-4_33
DO - 10.1007/978-3-642-32147-4_33
M3 - Conference contribution
AN - SCOPUS:84865205367
SN - 9783642321467
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 368
EP - 379
BT - Combinatorial Optimization - Second International Symposium, ISCO 2012, Revised Selected Papers
T2 - 2nd International Symposium on Combinatorial Optimization, ISCO 2012
Y2 - 19 April 2012 through 21 April 2012
ER -