Discrete Mathematics - Topics on domination
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Linear programming
The Minimum Satisfiability Problem
SIAM Journal on Discrete Mathematics
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Journal of Algorithms
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On the computational complexity of 2-interval pattern matching problems
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SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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Approximating the 2-interval pattern problem
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Using fractional primal-dual to schedule split intervals with demands
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Rounding to an integral program
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
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Theoretical Computer Science
Approximation algorithm for coloring of dotted interval graphs
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On the parameterized complexity of multiple-interval graph problems
Theoretical Computer Science
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Optimization problems in multiple-interval graphs
ACM Transactions on Algorithms (TALG)
On restrictions of balanced 2-interval graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
On the parameterized complexity of some optimization problems related to multiple-interval graphs
Theoretical Computer Science
On the parameterized complexity of some optimization problems related to multiple-interval graphs
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
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AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
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FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
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Minimum vertex cover in rectangle graphs
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Optimization problems in multiple subtree graphs
Discrete Applied Mathematics
Minimum vertex cover in rectangle graphs
Computational Geometry: Theory and Applications
ACM Transactions on Algorithms (TALG)
Online selection of intervals and t-intervals
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Optimization problems in multiple subtree graphs
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
The maximum clique problem in multiple interval graphs (extended abstract)
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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Multiple-interval graphs are a natural generalization of interval graphs where each vertex may have more then one interval associated with it. We initiate the study of optimization problems in multiple-interval graphs by considering three classical problems: MINIMUM VERTEX COVER, MINIMUM DOMINATING SET, and MAXIMUM CLIQUE. We describe applications for each one of these problems, and then proceed to discuss approximation algorithms for them. Our results can be summarized as follows: Let t be the number of intervals associated with each vertex in a given multiple-interval graph. For MINIMUM VERTEX COVER, we give a (2--1/t)-approximation algorithm which equals the best known ratio for 2t--1 bounded degree graphs. Since these graphs are known to be included in multiple-interval graphs with t intervals associated to each vertex, this ratio is in some sense tight. Following this, we give a t2-approximation algorithm for MINIMUM DOMINATING SET which adapts well to more general variants of the problem. We then proceed to prove that MAXIMUM CLIQUE is NP-complete for the case of t = 3, and provide a (t2--t+1)/2-approximation algorithm for the problem, using recent bounds proven for the so-called transversal number of t-interval families.