Fast approximation algorithms for fractional packing and covering problems
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A parallel approximation algorithm for positive linear programming
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Wireless Networks
On-line routing of virtual circuits with applications to load balancing and machine scheduling
Journal of the ACM (JACM)
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
Minimizing Congestion in General Networks
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On-Line Routing in All-Optical Networks
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
A practical algorithm for constructing oblivious routing schemes
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
A polynomial-time tree decomposition to minimize congestion
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Optimal oblivious routing in polynomial time
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Exploiting Locality for Data Management in Systems of Limited Bandwidth
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Approximating a Finite Metric by a Small Number of Tree Metrics
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Proceedings of the 2003 conference on Applications, technologies, architectures, and protocols for computer communications
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Sequential and Parallel Algorithms for Mixed Packing and Covering
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A general approach to online network optimization problems
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Euclidean distortion and the sparsest cut
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Approximating the k-multicut problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
The geometry of graphs and some of its algorithmic applications
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Approximation algorithms for requirement cut on graphs
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Partitioning graphs into balanced components
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Survey on Oblivious Routing Strategies
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Electric Routing and Concurrent Flow Cutting
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Thresholded covering algorithms for robust and max-min optimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Vertex sparsifiers: new results from old techniques
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Electric routing and concurrent flow cutting
Theoretical Computer Science
An O(n4) time algorithm to compute the bisection width of solid grid graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
Center-based clustering under perturbation stability
Information Processing Letters
Approximation algorithms and hardness of the k-route cut problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
An approximation algorithm for the Generalized k-Multicut problem
Discrete Applied Mathematics
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
Approximation algorithms for semi-random partitioning problems
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Approximation algorithms for fragmenting a graph against a stochastically-located threat
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Advantage of overlapping clusters for minimizing conductance
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Oblivious low-congestion multicast routing in wireless networks
Proceedings of the thirteenth ACM international symposium on Mobile Ad Hoc Networking and Computing
Towards a statistical characterization of the competitiveness of oblivious routing
Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE joint international conference on Measurement and Modeling of Computer Systems
Theoretical Computer Science
Submodular Approximation: Sampling-based Algorithms and Lower Bounds
SIAM Journal on Computing
Fast balanced partitioning is hard even on grids and trees
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Journal of the ACM (JACM)
Is information-centric multi-tree routing feasible?
Proceedings of the 3rd ACM SIGCOMM workshop on Information-centric networking
Hi-index | 0.00 |
Hierarchical graph decompositions play an important role in the design of approximation and online algorithms for graph problems. This is mainly due to the fact that the results concerning the approximation of metric spaces by tree metrics (e.g. [10,11,14,16]) depend on hierarchical graph decompositions. In this line of work a probability distribution over tree graphs is constructed from a given input graph, in such a way that the tree distances closely resemble the distances in the original graph. This allows it, to solve many problems with a distance-based cost function on trees, and then transfer the tree solution to general undirected graphs with only a logarithmic loss in the performance guarantee. The results about oblivious routing [30,22] in general undirected graphs are based on hierarchical decompositions of a different type in the sense that they are aiming to approximate the bottlenecks in the network (instead of the point-to-point distances). We call such decompositions cut-based decompositions. It has been shown that they also can be used to design approximation and online algorithms for a wide variety of different problems, but at the current state of the art the performance guarantee goes down by an O(log2n log log n)-factor when making the transition from tree networks to general graphs. In this paper we show how to construct cut-based decompositions that only result in a logarithmic loss in performance, which is asymptotically optimal. Remarkably, one major ingredient of our proof is a distance-based decomposition scheme due to Fakcharoenphol, Rao and Talwar [16]. This shows an interesting relationship between these seemingly different decomposition techniques. The main applications of the new decomposition are an optimal O(log n)-competitive algorithm for oblivious routing in general undirected graphs, and an O(log n)-approximation for Minimum Bisection, which improves the O(log1.5n) approximation by Feige and Krauthgamer [17].