In routing games, agents pick routes through a network to minimize their own delay. A primary concern for the network designer in routing games is the average agent delay at equilibrium. A number of methods to control this average delay have received substantial attention, including network tolls, Stackelberg routing, and edge removal. A related approach with arguably greater practical relevance is that of making investments in improvements to the edges of the network, so that, for a given investment budget, the average delay at equilibrium in the improved network is minimized. This problem has received considerable attention in the literature on transportation research. We study a model for this problem introduced in transportation research literature, and present both hardness results and algorithms that obtain tight performance guarantees. In general graphs, we show that a simple algorithm obtains a 4/3-approximation for affine delay functions and an O(p/logp)-approximation for polynomial delay functions of degree p. For affine delays, we show that it is NP-hard to improve upon the 4/3 approximation. Motivated by the practical relevance of the problem, we consider restricted topologies to obtain better bounds. In series-parallel graphs, we show that the problem is still NP-hard. However, we show that there is an FPTAS in this case. Finally, for graphs consisting of parallel paths, we show that an optimal allocation can be obtained in polynomial time.
|Original language||American English|
|Title of host publication||Integer Programming and Combinatorial Optimization - 17th International Conference, IPCO 2014, Proceedings|
|Number of pages||12|
|State||Published - 2014|
|Event||17th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2014 - Bonn, Germany|
Duration: 23 Jun 2014 → 25 Jun 2014
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||17th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2014|
|Period||23/06/14 → 25/06/14|
Bibliographical noteFunding Information:
Supported in part by NSF Awards 1038578 and 1319745, an NSF CAREER Award (1254169), the Charles Lee Powell Foundation, and a Microsoft Research Faculty Fellowship.