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
On-line k-Truck Problem and Its Competitive Algorithms
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Embedding k-outerplanar graphs into ℓ1
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
A Variant of the Arrow Distributed Directory with Low Average Complexity
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Carrying Umbrellas: An Online Relocation Problem on Graphs
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Minimum Restricted Diameter Spanning Trees
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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FOCS '99 Proceedings of the 40th 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
Minimum restricted diameter spanning trees
Discrete Applied Mathematics
Approximating metrics by tree metrics
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STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Lower bounds for graph embeddings and combinatorial preconditioners
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Sparse source-wise and pair-wise distance preservers
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Finding effective support-tree preconditioners
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Metric Embeddings with Relaxed Guarantees
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Improved embeddings of graph metrics into random trees
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
Scalable data aggregation for dynamic events in sensor networks
Proceedings of the 4th international conference on Embedded networked sensor systems
Probabilistic embeddings of bounded genus graphs into planar graphs
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Local embeddings of metric spaces
Proceedings of the thirty-ninth 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
The zoo of tree spanner problems
Discrete Applied Mathematics
A randomized algorithm for the on-line weighted bipartite matching problem
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APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Maximum Gradient Embeddings and Monotone Clustering
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Counting distance permutations
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Randomized algorithm for the k-server problem on decomposable spaces
Journal of Discrete Algorithms
On the bias and performance of the edge-set encoding
IEEE Transactions on Evolutionary Computation
Minimum cut bases in undirected networks
Discrete Applied Mathematics
Benchmarks for strictly fundamental cycle bases
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Subgraph sparsification and nearly optimal ultrasparsifiers
Proceedings of the forty-second ACM symposium on Theory of computing
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
A Tight Upper Bound on the Probabilistic Embedding of Series-Parallel Graphs
SIAM Journal on Discrete Mathematics
Near linear-work parallel SDD solvers, low-diameter decomposition, and low-stretch subgraphs
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Online algorithms for the vehicle scheduling problem with time objective
WINE'05 Proceedings of the First international conference on Internet and Network Economics
A graph-theoretic network security game
WINE'05 Proceedings of the First international conference on Internet and Network Economics
On the online dial-a-ride problem with time-windows
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
The laplacian paradigm: emerging algorithms for massive graphs
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Using petal-decompositions to build a low stretch spanning tree
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Survey: Cycle bases in graphs characterization, algorithms, complexity, and applications
Computer Science Review
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Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
A fast solver for a class of linear systems
Communications of the ACM
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ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Approximation algorithms and hardness results for shortest path based graph orientations
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Generalized subgraph preconditioners for large-scale bundle adjustment
Proceedings of the 15th international conference on Theoretical Foundations of Computer Vision: outdoor and large-scale real-world scene analysis
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
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This paper investigates a zero-sum game played on a weighted connected graph $G$ between two players, the tree player and the edge player. At each play, the tree player chooses a spanning tree $T$ and the edge player chooses an edge $e$. The payoff to the edge player is $cost(T,e)$, defined as follows: If $e$ lies in the tree $T$ then $cost(T,e)=0$; if $e$ does not lie in the tree then $cost(T,e) = cycle(T,e)/w(e)$, where $w(e)$ is the weight of edge $e$ and $cycle(T,e)$ is the weight of the unique cycle formed when edge $e$ is added to the tree $T$. The main result is that the value of the game on any $n$-vertex graph is bounded above by $\exp(O(\sqrt{\log n \log\log n}))$. It is conjectured that the value of the game is $O(\log n)$. The game arises in connection with the $k$-server problem on a road network; i.e., a metric space that can be represented as a multigraph $G$ in which each edge $e$ represents a road of length $w(e)$. It is shown that, if the value of the game on $G$ is $Val(G,w)$, then there is a randomized strategy that achieves a competitive ratio of $k(1 + Val(G,w))$ against any oblivious adversary. Thus, on any $n$-vertex road network, there is a randomized algorithm for the $k$-server problem that is $k\cdot\exp(O(\sqrt{\log n \log\log n}))$ competitive against oblivious adversaries. At the heart of the analysis of the game is an algorithm that provides an approximate solution for the simple network design problem. Specifically, for any $n$-vertex weighted, connected multigraph, the algorithm constructs a spanning tree $T$ such that the average, over all edges $e$, of $cost(T,e)$ is less than or equal to $\exp(O(\sqrt{\log n \log\log n}))$. This result has potential application to the design of communication networks. It also improves substantially known estimates concerning the existence of a sparse basis for the cycle space of a graph.