A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
Rounding via trees: deterministic approximation algorithms for group Steiner trees and k-median
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth 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
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximating Minimum Max-Stretch spanning Trees on unweighted graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A tight upper bound on the probabilistic embedding of series-parallel graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Advances in metric embedding theory
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Embedding metrics into ultrametrics and graphs into spanning trees with constant average distortion
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for embedding general metrics into trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Graph sparsification by effective resistances
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Nearly Tight Low Stretch Spanning Trees
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
A faster algorithm for the single source shortest path problem with few distinct positive lengths
Journal of Discrete Algorithms
Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Approaching Optimality for Solving SDD Linear Systems
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Electrical flows, laplacian systems, and faster approximation of maximum flow in undirected graphs
Proceedings of the forty-third annual ACM symposium on Theory of computing
A Nearly-m log n Time Solver for SDD Linear Systems
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
A fast solver for a class of linear systems
Communications of the ACM
Algorithms, graph theory, and the solution of laplacian linear equations
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Parallel graph decompositions using random shifts
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
A simple, combinatorial algorithm for solving SDD systems in nearly-linear time
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
| Hi-index | 0.02 |
We prove that any graph G=(V,E) with n points and m edges has a spanning tree T such that ∑(u,v)∈ E(G)dT(u,v) = O(m log n log log n). Moreover such a tree can be found in time O(m log n log log n). Our result is obtained using a new petal-decomposition approach which guarantees that the radius of each cluster in the tree is at most 4 times the radius of the induced subgraph of the cluster in the original graph.