On chromatic sums and distributed resource allocation
Information and Computation
Strengthening integrality gaps for capacitated network design and covering problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
Approximation algorithms for the covering Steiner problem
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
Polylogarithmic inapproximability
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Paths, Trees, and Minimum Latency Tours
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Approximating Min Sum Set Cover
Algorithmica
A Recursive Greedy Algorithm for Walks in Directed Graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Optimization of continuous queries with shared expensive filters
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The k-traveling repairmen problem
ACM Transactions on Algorithms (TALG)
Near-optimal algorithms for shared filter evaluation in data stream systems
Proceedings of the 2008 ACM SIGMOD international conference on Management of data
Proceedings of the forty-first annual ACM symposium on Theory of computing
A greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
Approximation algorithms for sequencing problems
Approximation algorithms for sequencing problems
Detecting high log-densities: an O(n¼) approximation for densest k-subgraph
Proceedings of the forty-second ACM symposium on Theory of computing
A constant factor approximation algorithm for generalized min-sum set cover
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximation algorithms for optimal decision trees and adaptive TSP problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Ranking with submodular valuations
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Stochastic covering and adaptivity
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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We study the submodular ranking problem in the presence of metric costs. The input to the minimum latency submodular cover (MLSC) problem consists of a metric (V,d) with source r∈V and m monotone submodular functions f1, f2, ..., fm: 2V→[0,1]. The goal is to find a path originating at r that minimizes the total cover time of all functions; the cover time of function fi is the smallest value t such that fi has value one for the vertices visited within distance t along the path. This generalizes many previously studied problems, such as submodular ranking [1] when the metric is uniform, and group Steiner tree [14] when m=1 and f1 is a coverage function. We give a polynomial time $O(\log \frac{1}{\epsilon } \cdot \log^{2+\delta} |V|)$-approximation algorithm for MLSC, where ε0 is the smallest non-zero marginal increase of any $\{f_i\}_{i=1}^m$ and δ0 is any constant. This result is enabled by a simpler analysis of the submodular ranking algorithm from [1]. We also consider the stochastic submodular ranking problem where elements V have random instantiations, and obtain an adaptive algorithm with an O(log1/ ε) approximation ratio, which is best possible. This result also generalizes several previously studied stochastic problems, eg. adaptive set cover [15] and shared filter evaluation [24,23].