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
Approximation algorithms for directed Steiner problems
Journal of Algorithms
A 2 + ε approximation algorithm for the k-MST problem
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
A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
Approximation algorithms for the covering Steiner problem
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
Integrality ratio for group Steiner trees and directed steiner trees
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On Network Design Problems: Fixed Cost Flows and the Covering Steiner Problem
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
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
Approximation Algorithms for Orienteering and Discounted-Reward TSP
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Approximation Algorithms for Asymmetric TSP by Decomposing Directed Regular Multigraphs
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 greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
The orienteering problem in the plane revisited
Proceedings of the twenty-second annual symposium on Computational geometry
Improved algorithms for orienteering and related problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating a vehicle scheduling problem with time windows and handling times
Theoretical Computer Science
Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
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
Nonmyopic informative path planning in spatio-temporal models
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Near-optimal observation selection using submodular functions
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Efficient informative sensing using multiple robots
Journal of Artificial Intelligence Research
Efficient planning of informative paths for multiple robots
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Efficient viewpoint assignment for urban texture documentation
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Nonmyopic adaptive informative path planning for multiple robots
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Constructing travel itineraries from tagged geo-temporal breadcrumbs
Proceedings of the 19th international conference on World wide web
Automatic construction of travel itineraries using social breadcrumbs
Proceedings of the 21st ACM conference on Hypertext and hypermedia
The effective application of a new approach to the generalized orienteering problem
Journal of Heuristics
Approximation algorithms for the directed k-tour and k-stroll problems
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Robust sensor placements at informative and communication-efficient locations
ACM Transactions on Sensor Networks (TOSN)
A unified submodular framework for multimodal IC Trojan detection
IH'10 Proceedings of the 12th international conference on Information hiding
Approximation algorithms for stochastic orienteering
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Trains of thought: generating information maps
Proceedings of the 21st international conference on World Wide Web
Improved algorithms for orienteering and related problems
ACM Transactions on Algorithms (TALG)
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Submodular Approximation: Sampling-based Algorithms and Lower Bounds
SIAM Journal on Computing
Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
SIAM Journal on Computing
Stochastic vehicle routing with recourse
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Minimum latency submodular cover
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Multi-day and multi-stay travel planning using geo-tagged photos
Proceedings of the Second ACM SIGSPATIAL International Workshop on Crowdsourced and Volunteered Geographic Information
Customized tour recommendations in urban areas
Proceedings of the 7th ACM international conference on Web search and data mining
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Given an arc-weighted directed graph G = (V, A, \ell) and a pair of nodes s, t, we seek to find an s-t walk of length at most B that maximizes some given function f of the set of nodes visited by the walk. The simplest case is when we seek to maximize the number of nodes visited: this is called the orienteering problem. Our main result is a quasipolynomial time algorithm that yields an O(log OPT) approximation for this problem when f is a given submodular set function. We then extend it to the case when a node v is counted as visited only if the walk reaches v in its time window [R(v),D(v)]. We apply the algorithm to obtain several new results. First, we obtain an O(log OPT) approximation for a generalization of the orienteering problem in which the profit for visiting each node may vary arbitrarily with time. This captures the time window problem considered earlier for which, even in undirected graphs, the best approximation ratio known [4] is O(\log^2 OPT). The second application is an O(\log^2 k) approximation for the k-TSP problem in directed graphs (satisfying asymmetric triangle inequality). This is the first non-trivial approximation algorithm for this problem. The third application is an O(\log^2 k) approximation (in quasi-poly time) for the group Steiner problem in undirected graphs where k is the number of groups. This improves earlier ratios [15, 19, 8]] by a logarithmic factor and almost matches the inapproximability threshold on trees [20]. This connection to group Steiner trees also enables us to prove that the problem we consider is hard to approximate to a ratio better than \Omega(\log^{1 - \varepsilon} OPT), even in undirected graphs.