When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Approximation algorithms
A priori optimization for the probabilistic maximum independent set problem
Theoretical Computer Science
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Boosted sampling: approximation algorithms for stochastic optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
An Edge in Time Saves Nine: LP Rounding Approximation Algorithms for Stochastic Network Design
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Simple cost sharing schemes for multicommodity rent-or-buy and stochastic Steiner tree
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On the probabilistic minimum coloring and minimum k-coloring
Discrete Applied Mathematics
Stochastic steiner trees without a root
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On two-stage stochastic minimum spanning trees
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
What about wednesday? approximation algorithms for multistage stochastic optimization
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
Vertex-Uncertainty in Graph-Problems
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
On the probabilistic min spanning tree Problem
Journal of Mathematical Modelling and Algorithms
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We consider the problem of connecting given vertex pairs over a stochastic metric graph, each vertex of which has a probability of presence independently of all other vertices. Vertex pairs requiring connection are always present with probability 1. Our objective is to satisfy the connectivity requirements for every possibly materializable subgraph of the given metric graph, so as to optimize the expected total cost of edges used. This is a natural problem model for cost-efficient Steiner Forests on stochastic metric graphs, where uncertain availability of intermediate nodes requires fast adjustments of traffic forwarding. For this problem we allow a priori design decisions to be taken, that can be modified efficiently when an actual subgraph of the input graph materializes. We design a fast (almost linear time in the number of vertices) modification algorithm whose outcome we analyze probabilistically, and show that depending on the a priori decisions this algorithm yields 2 or 4 approximation factors of the optimum expected cost. We also show that our analysis of the algorithm is tight.