On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On-line routing in all-optical networks
Theoretical Computer Science
A constant factor approximation for the single sink edge installation problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Approximating the Single-Sink Link-Installation Problem in Network Design
SIAM Journal on Optimization
Simultaneous optimization for concave costs: single sink aggregation or single source buy-at-bulk
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Minimizing Congestion in General Networks
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A Constant-Factor Approximation Algorithm for the Multicommodity
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The Single-Sink Buy-at-Bulk LP Has Constant Integrality Gap
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
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
Simpler and better approximation algorithms for network design
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Cost-distance: two metric network design
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Building Steiner trees with incomplete global knowledge
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Hierarchical placement and network design problems
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Universal schemes for parallel communication
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
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
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
FOCS '03 Proceedings of the 44th Annual 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
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The all-or-nothing multicommodity flow problem
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Boosted sampling: approximation algorithms for stochastic optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Hardness of Buy-at-Bulk Network Design
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
On non-uniform multicommodity buy-at-bulk network design
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Universal approximations for TSP, Steiner tree, and set cover
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On hierarchical routing in doubling metrics
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the approximability of some network design problems
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
Improved lower and upper bounds for universal TSP in planar metrics
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximation via cost sharing: Simpler and better approximation algorithms for network design
Journal of the ACM (JACM)
Minimizing average latency in oblivious routing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Designing networks with good equilibria
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Maximum Gradient Embeddings and Monotone Clustering
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
Oblivious interference scheduling
Proceedings of the 28th ACM symposium on Principles of distributed computing
The online transportation problem: on the exponential boost of one extra server
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
DISC'09 Proceedings of the 23rd international conference on Distributed computing
Approximation algorithms for optimal decision trees and adaptive TSP problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Improved lower bounds for the universal and a priori TSP
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Threshold rules for online sample selection
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Designing Network Protocols for Good Equilibria
SIAM Journal on Computing
Oblivious buy-at-bulk in planar graphs
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Optimal lower bounds for universal and differentially private steiner trees and TSPs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Online cooperative cost sharing
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Algorithms for the universal and a priori TSP
Operations Research Letters
Hi-index | 0.00 |
Consider the following network design problem: given a network G = (V, E), source-sink pairs {si, ti} arrive and desire to send a unit of flow between themselves. The cost of the routing is this: if edge e carries a total of fe flow (from all the terminal pairs), the cost is given by Σ el(fe), where l is some concave cost function; the goal is to minimize the total cost incurred. However, we want the routing to be oblivious: when terminal pair {si, ti} makes its routing decisions, it does not know the current flow on the edges of the network, nor the identity of the other pairs in the system. Moreover, it does not even know the identity of the function l, merely knowing that l is a concave function of the total flow on the edge. How should it (obliviously) route its one unit of flow? Can we get competitive algorithms for this problem?In this paper, we develop a framework to model oblivious network design problems (of which the above problem is a special case), and give algorithms with poly-logarithmic competitive ratio for problems in this framework (and hence for this problem). Abstractly, given a problem like the one above, the solution is a multicommodity flow producing a "load" on each edge of Le = l(f1(e),f2(e), ..., fk(e)), and the total cost is given by an "aggregation function" agg (Le1,...,Lem) of the loads of all edges. Our goal is to develop oblivious algorithms that approximately minimize the total cost of the routing, knowing the aggregation function agg, but merely knowing that l lies in some class C, and having no other information about the current state of the network. Hence we want algorithms that are simultaneously "function-oblivious" as well as "traffic-oblivious".The aggregation functions we consider are the max and σ objective functions, which correspond to the well-known measures of congestion and total cost of a network; in this paper, we prove the following:• If the aggregation function is Σ, we give an oblivious algorithm with O(log2 n) competitive ratio whenever the load function l is in the class of monotone sub-additive functions. (Recall that our algorithm is also "function-oblivious"; it works whenever each edge has a load function l in the class.)• For the case when the aggregation function is max, we give an oblivious algorithm with O(log2 n log log n) competitive ratio, when the load function l is a norm; we also show that such a competitive ratio is not possible for general sub-additive functions.These are the first such general results about oblivious algorithms for network design problems, and we hope the ideas and techniques will lead to more and improved results in this area.