Improved algorithms for orienteering and related problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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
Online story scheduling in web advertising
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Multi-armed Bandits with Metric Switching Costs
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Multi-robot routing with linear decreasing rewards over time
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Dynamic Vehicle Routing with Priority Classes of Stochastic Demands
SIAM Journal on Control and Optimization
Capacitated vehicle routing with non-uniform speeds
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Exploring and triangulating a region by a swarm of robots
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Approximation algorithms for stochastic orienteering
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Prize-collecting Steiner problems on planar graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The school bus problem on trees
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Improved algorithms for orienteering and related problems
ACM Transactions on Algorithms (TALG)
Multiple agents maximum collection problem with time dependent rewards
Computers and Industrial Engineering
Now or later?: delaying data transfer in time-critical aerial communication
Proceedings of the ninth ACM conference on Emerging networking experiments and technologies
Hi-index | 0.00 |
In this paper, we give the first constant-factor approximation algorithm for the rooted Orienteering problem, as well as a new problem that we call the Discounted-Reward traveling salesman problem (TSP), motivated by robot navigation. In both problems, we are given a graph with lengths on edges and rewards on nodes, and a start node $s$. In the Orienteering problem, the goal is to find a path starting at $s$ that maximizes the reward collected, subject to a hard limit on the total length of the path. In the Discounted-Reward TSP, instead of a length limit we are given a discount factor $\gamma$, and the goal is to maximize the total discounted reward collected, where the reward for a node reached at time $t$ is discounted by $\gamma^t$. This problem is motivated by an approximation to a planning problem in the Markov decision process (MDP) framework under the commonly employed infinite horizon discounted reward optimality criterion. The approximation arises from a need to deal with exponentially large state spaces that emerge when trying to model one-time events and nonrepeatable rewards (such as for package deliveries). We also consider tree and multiple-path variants of these problems and provide approximations for those as well. Although the unrooted Orienteering problem, where there is no fixed start node $s$, has been known to be approximable using algorithms for related problems such as $k$-TSP (in which the amount of reward to be collected is fixed and the total length is approximately minimized), ours is the first to approximate the rooted question, solving an open problem in [E. M. Arkin, J. S. B. Mitchell, and G. Narasimhan, Proceedings of the $14$th ACM Symposium on Computational Geometry, 1998, pp. 307-316] and [B. Awerbuch, Y. Azar, A. Blum, and S. Vempala, SIAM J. Comput., 28 (1998), pp. 254-262]. We complement our approximation result for Orienteering by showing that the problem is APX-hard.