Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
On-line algorithms for Steiner tree problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On-line generalized Steiner problem
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
Approximation algorithms
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
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
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
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On the competitive ratio for online facility location
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Set connectivity problems in undirected graphs and the directed Steiner network problem
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Non-cooperative Cost Sharing Games Via Subsidies
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Combinatorial optimization in system configuration design
Automation and Remote Control
Online Primal-Dual Algorithms for Covering and Packing
Mathematics of Operations Research
The Design of Competitive Online Algorithms via a Primal: Dual Approach
Foundations and Trends® in Theoretical Computer Science
Admission control to minimize rejections and online set cover with repetitions
ACM Transactions on Algorithms (TALG)
Inferring social networks from outbreaks
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
Set connectivity problems in undirected graphs and the directed steiner network problem
ACM Transactions on Algorithms (TALG)
Online and incremental algorithms for facility location
ACM SIGACT News
Approximating k-generalized connectivity via collapsing HSTs
Journal of Combinatorial Optimization
Frequency capping in online advertising
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Approximating sparse covering integer programs online
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
A distributed algorithm for large-scale generalized matching
Proceedings of the VLDB Endowment
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We study a wide range of online graph and network optimization problems, focusing on problems that arise in the study of connectivity and cuts in graphs. In a general online network design problem, we have a communication network known to the algorithm in advance. What is not known in advance are the connectivity (bandwidth) or cut demands between vertices in the network which arrive online.We develop a unified framework for designing online algorithms for problems involving connectivity and cuts. We first present a general O(log m)-competitive deterministic algorithm for generating a fractional solution that satisfies the online connectivity or cut demands, where m is the number of edges in the graph. This may be of independent interest for solving fractional online bandwidth allocation problems, and is applicable to both directed and undirected graphs. We then show how to obtain integral solutions via an online rounding of the fractional solution. This part of the framework is problem dependent, and applies various tools including results on approximate max-flow min-cut for multicommodity flow, the Hierarchically Separated Trees (HST) method and its extensions, certain rounding techniques for dependent variables, and Räcke's new hierarchical decomposition of graphs.Specifically, our results for the integral case include an O(log mlog n)-competitive randomized algorithm for the online nonmetric facility location problem and for a generalization of the problem called the multicast problem. In the nonmetric facility location problem, m is the number of facilities and n is the number of clients. The competitive ratio is nearly tight. We also present an O(log2nlog k)-competitive randomized algorithm for the online group Steiner problem in trees and an O(log3nlog k)-competitive randomized algorithm for the problem in general graphs, where n is the number of vertices in the graph and k is the number of groups. Finally, we design a deterministic O(log3nlog log n)-competitive algorithm for the online multi-cut problem.