Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
Polynomial time approximation schemes for dense instances of NP-hard problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Towards a syntactic characterization of PTAS
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
A note on approximating Max-Bisection on regular graphs
Information Processing Letters
On the complexity of the maximum cut problem
Nordic Journal of Computing
Approximation Algorithms for Maximum Coverage and Max Cut with Given Sizes of Parts
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
A Unified Approach to Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
A polylogarithmic approximation of the minimum bisection
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Approximation algorithms for NP-complete problems on planar graphs
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Approximability of the Minimum Bisection Problem: An Algorithmic Challenge
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Approximating Bounded Degree Instances of NP-Hard Problems
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Approximation Algorithms for Fractional Covering and Packing Problems, and Applications
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Some results on matchgates and holographic algorithms
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
The complexity of finding uniform sparsest cuts in various graph classes
Journal of Discrete Algorithms
Approximation Algorithms for MAX-BISECTION on Low Degree Regular Graphs
Fundamenta Informaticae
| Hi-index | 0.00 |
The Max-Bisection and Min-Bisection problems are to find a partition of the vertices of a graph into two equal size subsets that respectively maximizes or minimizes the number of edges with endpoints in both subsets. We design the first polynomial time approximation scheme for the Max-Bisection problem on arbitrary planar graphs solving a long time standing open problem. The method of solution involves designing exact polynomial time algorithms for computing optimal partitions of bounded treewidth graphs, in particular Max- and Min-Bisection, which could be of independent interest. Using similar method we design also the first polynomial time approximation scheme for Max-Bisection on unit disk graphs (which could be easily extended to other geometrically defined graphs).