Analyzing the Held-Karp TSP bound: a monotonicity property with application
Information Processing Letters
Survivable networks, linear programming relaxations and the parsimonious property
Mathematical Programming: Series A and B
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Rounding via trees: deterministic approximation algorithms for group Steiner trees and k-median
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
An improved approximation ratio for the minimum latency 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
The vehicle routing problem
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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
The k-traveling repairmen problem
ACM Transactions on Algorithms (TALG)
A Faster, Better Approximation Algorithm for the Minimum Latency Problem
SIAM Journal on Computing
An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
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
Approximation algorithms for sequencing problems
Approximation algorithms for sequencing problems
Approximation algorithms for optimal decision trees and adaptive TSP problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Minimum latency submodular cover
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Hi-index | 0.00 |
We introduce a problem that is a common generalization of the uncapacitated facility location and minimum latency (ML) problems, where facilities need to be opened to serve clients and also need to be sequentially activated before they can provide service. Formally, we are given a set F of n facilities with facility-opening costs fi, a set D of m clients, connection costs cij specifying the cost of assigning a client j to a facility i, a root node r denoting the depot, and a time metric d on F∪{r}. Our goal is to open a subset F of facilities, find a path P starting at r and spanning F to activate the open facilities, and connect each client j to a facility φ(j) ε F, so as to minimize Σi∈Ffi + Σj∈D(Cφ(j),j +tj), where tj is the time taken to reach φ(j) along path P. We call this the minimum latency uncapacitated facility location (MLUFL) problem. Our main result is an O(log n ċ max(log n, logm))-approximation for MLUFL. We also show that any improvement in this approximation guarantee, implies an improvement in the (current-best) approximation factor for group Steiner tree. We obtain constant approximations for two natural special cases of the problem: (a) related MLUFL (metric connection costs that are a scalar multiple of the time metric); (b) metric uniform MLUFL (metric connection costs, uniform time-metric). Our LP-based methods are versatile and easily adapted to yield approximation guarantees for MLUFL in various more general settings, such as (i) when the latency-cost of a client is a function of the delay faced by the facility to which it is connected; and (ii) the k-route version, where k vehicles are routed in parallel to activate the open facilities. Our LP-based understanding of MLUFL also offers some LP-based insights into ML, which we believe is a promising direction for obtaining improvements for ML.