On an Optimal Split Tree Problem
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
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
A Recursive Greedy Algorithm for Walks in Directed Graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms for budgeted learning problems
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
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
Approximating Optimal Binary Decision Trees
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Multi-armed Bandits with Metric Switching Costs
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Approximating Matches Made in Heaven
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Approximation algorithms for optimal decision trees and adaptive TSP problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Approximation Algorithms for Correlated Knapsacks and Non-martingale Bandits
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Improved approximation results for stochastic knapsack problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Stochastic vehicle routing with recourse
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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In the Stochastic Orienteering problem, we are given a metric, where each node also has a job located there with some deterministic reward and a random size. (Think of the jobs as being chores one needs to run, and the sizes as the amount of time it takes to do the chore.) The goal is to adaptively decide which nodes to visit to maximize total expected reward, subject to the constraint that the total distance traveled plus the total size of jobs processed is at most a given budget of B. (I.e., we get reward for all those chores we finish by the end of the day). The (random) size of a job is not known until it is completely processed. Hence the problem combines aspects of both the stochastic knapsack problem with uncertain item sizes and the deterministic orienteering problem of using a limited travel time to maximize gathered rewards located at nodes. In this paper, we present a constant-factor approximation algorithm for the best non-adaptive policy for the Stochastic Orienteering problem. We also show a small adaptivity gap---i.e., the existence of a non-adaptive policy whose reward is at least an Ω(1/log log B) fraction of the optimal expected reward---and hence we also get an O(log log B)-approximation algorithm for the adaptive problem. Finally we address the case when the node rewards are also random and could be correlated with the waiting time, and give a non-adaptive policy which is an O(log n logB)-approximation to the best adaptive policy on n-node metrics with budget B.