Edge separators of planar and outerplanar graphs with applications
Journal of Algorithms
Excluded minors, network decomposition, and multicommodity flow
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Finding minimum-quotient cuts in planar graphs
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Parallel approximation schemes for problems on planar graphs
Acta Informatica
How Good is Recursive Bisection?
SIAM Journal on Scientific Computing
Highly connected sets and the excluded grid theorem
Journal of Combinatorial Theory Series B
Fast Approximate Graph Partitioning Algorithms
SIAM Journal on Computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
IEEE Transactions on Pattern Analysis and Machine Intelligence
On partitioning a graph: a theoretical and empirical study.
On partitioning a graph: a theoretical and empirical study.
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Theory of Computing Systems
Optimal hierarchical decompositions for congestion minimization in networks
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
PT-Scotch: A tool for efficient parallel graph ordering
Parallel Computing
Partitioning graphs into balanced components
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Multi-level µ-finite element analysis for human bone structures
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
An O(n4) time algorithm to compute the bisection width of solid grid graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
Restricted cuts for bisections in solid grids: a proof via polygons
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
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Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfactory approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that this tradeoff between runtime and solution quality is unavoidable. For the problem a minimum number of edges in a graph need to be found that, when cut, partition the vertices into k equal-sized sets. We develop a general reduction which identifies some sufficient conditions on the considered graph class in order to prove the hardness of the problem. We focus on two combinatorially simple but very different classes, namely trees and solid grid graphs. The latter are finite connected subgraphs of the infinite two-dimensional grid without holes. We apply the reduction to show that for solid grid graphs it is NP-hard to approximate the optimum number of cut edges within any satisfactory ratio. We also consider solutions in which the sets may deviate from being equal-sized. Our reduction is applied to grids and trees to prove that no fully polynomial time algorithm exists that computes solutions in which the sets are arbitrarily close to equal-sized. This is true even if the number of edges cut is allowed to increase when the limit on the set sizes decreases. These are the first bicriteria inapproximability results for the k-BALANCED PARTITIONING problem.