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Annals of Operations Research
The traveling salesman problem with distances one and two
Mathematics of Operations Research
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Operations Research
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
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SIAM Journal on Computing
A 2.5-factor approximation algorithm for the k-MST problem
Information Processing Letters
Approximation schemes for minimum latency problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
P-Complete Approximation Problems
Journal of the ACM (JACM)
A 2 + ε approximation algorithm for the k-MST problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Polynomial time algorithms for some minimum latency problems
Information Processing Letters
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Theoretical Computer Science
Approximation algorithms for time-dependent orienteering
Information Processing Letters
The k-traveling repairman problem
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
The Minimum Latency Problem Is NP-Hard for Weighted Trees
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
The Dynamic Vertex Minimum Problem and Its Application to Clustering-Type Approximation Algorithms
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
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FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
The k-traveling repairman problem
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Exact algorithms for the minimum latency problem
Information Processing Letters
A general approach for incremental approximation and hierarchical clustering
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Playing games in many possible worlds
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Approximating the k-traveling repairman problem with repairtimes
Journal of Discrete Algorithms
The k-traveling repairmen problem
ACM Transactions on Algorithms (TALG)
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Discrete Applied Mathematics
Multi-robot routing with linear decreasing rewards over time
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Exact algorithms for the minimum latency problem
Information Processing Letters
Improved genetic algorithm for minimum latency problem
Proceedings of the 2010 Symposium on Information and Communication Technology
Faster and simpler approximation of stable matchings
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
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In this paper, we give a 9.28-approximation algorithm for the minimum latency problem that uses only O(n log n) calls to the prize-collecting Steiner tree (PCST) subroutine of Goemans and Williamson. A previous algorithm of Goemans and Kleinberg for the minimum latency problem requires an approximation algorithm for the k-MST problem which is called as a black box. Their algorithm can achieve a performance guarantee of 10.77 while making O(n2 log n) PCST calls (via a k-MST algorithm of Garg), or a performance guarantee of 7.18 + ε while using nO(1/ε) PCST calls (via a k-MST algorithm of Arora and Karakostas). In order to match our approximation ratio (i.e. setting ε = 2.10), the latter version requires O(n5 log2 n) PCST calls, so our running time bound is faster by a factor of Θ(n4 log n). Since PCST can be implemented to run in O(n2) time, the overall running time of our algorithm is O(n3 log n).The basic idea for our improvement is that we do not treat the k-MST algorithm as a black box. Thus we are able to take advantage of some situations in which the PCST subroutine delivers a k-MST with an improved performance guarantee.