Stability in circular arc graphs
Journal of Algorithms
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Linear time algorithms on circular-arc graphs
Information Processing Letters
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
Label placement by maximum independent set in rectangles
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
Dotted interval graphs and high throughput genotyping
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Polynomial-Time Approximation Schemes for Geometric Intersection Graphs
SIAM Journal on Computing
SIAM Journal on Computing
Approximation algorithm for coloring of dotted interval graphs
Information Processing Letters
Maximum independent set of rectangles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximating minimum coloring and maximum independent set in dotted interval graphs
Information Processing Letters
Optimization problems in multiple-interval graphs
ACM Transactions on Algorithms (TALG)
Optimization problems in multiple subtree graphs
Discrete Applied Mathematics
Minimum vertex cover in rectangle graphs
Computational Geometry: Theory and Applications
Better approximation schemes for disk graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Approximation algorithms for unit disk graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
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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 ε0 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.