Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Resource-constrained geometric network optimization
Proceedings of the fourteenth annual symposium on Computational geometry
New Approximation Guarantees for Minimum-Weight k-Trees and Prize-Collecting Salesmen
SIAM Journal on Computing
A constant-factor approximation algorithm for the k-MST problem
Journal of Computer and System Sciences
The vehicle routing problem
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Paths, Trees, and Minimum Latency Tours
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms for deadline-TSP and vehicle routing with time-windows
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Saving an epsilon: a 2-approximation for the k-MST problem in graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A Recursive Greedy Algorithm for Walks in Directed Graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A 2 + ɛ approximation algorithm for the k-MST problem
Mathematical Programming: Series A and B
Approximation Algorithms for Orienteering and Discounted-Reward TSP
SIAM Journal on Computing
Improved algorithms for orienteering and related problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The Euclidean Orienteering Problem Revisited
SIAM Journal on Computing
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
Poly-logarithmic Approximation Algorithms for Directed Vehicle Routing Problems
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
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In this article, we consider the orienteering problem in undirected and directed graphs and obtain improved approximation algorithms. The point to point-orienteering problem is the following: Given an edge-weighted graph G=(V, E) (directed or undirected), two nodes s, t ∈ V and a time limit B, find an s-t walk in G of total length at most B that maximizes the number of distinct nodes visited by the walk. This problem is closely related to tour problems such as TSP as well as network design problems such as k-MST. Orienteering with time-windows is the more general problem in which each node v has a specified time-window [R(v), D(v)] and a node v is counted as visited by the walk only if v is visited during its time-window. We design new and improved algorithms for the orienteering problem and orienteering with time-windows. Our main results are the following: — A (2+ε) approximation for orienteering in undirected graphs, improving upon the 3-approximation of Bansal et al. [2004]. — An O(log2 OPT) approximation for orienteering in directed graphs, where OPT ≤ n is the number of vertices visited by an optimal solution. Previously, only a quasipolynomial-time algorithm due to Chekuri and Pál [2005] achieved a polylogarithmic approximation (a ratio of O(log OPT)). — Given an α approximation for orienteering, we show an O(α ċ max{log OPT, log lmax/lmin}) approximation for orienteering with time-windows, where lmax and lmin are the lengths of the longest and shortest time-windows respectively.