Computational Complexity, Fairness, and the Price of Anarchy of the Maximum Latency Problem
We study the problem of minimizing the maximum latency of flows in networks with congestion. We show that this problem is NP-hard, even when all arc latency functions are linear and there is a single source and sink. Still, one can prove that an optimal flow and an equilibrium flow share a desirable...
| Main Authors: | , , |
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| Format: | Working Paper |
| Language: | en_US |
| Published: |
2004
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| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/5051 |
| _version_ | 1826215231331762176 |
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| author | Correa, Jose R. Schulz, Andreas S. Stier Moses, Nicolas E. |
| author_facet | Correa, Jose R. Schulz, Andreas S. Stier Moses, Nicolas E. |
| author_sort | Correa, Jose R. |
| collection | MIT |
| description | We study the problem of minimizing the maximum latency of flows in networks with congestion. We show that this problem is NP-hard, even when all arc latency functions are linear and there is a single source and sink. Still, one can prove that an optimal flow and an equilibrium flow share a desirable property in this situation: all flow-carrying paths have the same length; i.e., these solutions are "fair," which is in general not true for the optimal flow in networks with nonlinear latency functions. In addition, the maximum latency of the Nash equilibrium, which can be computed efficiently, is within a constant factor of that of an optimal solution. That is, the so-called price of anarchy is bounded. In contrast, we present a family of instances that shows that the price of anarchy is unbounded for instances with multiple sources and a single sink, even in networks with linear latencies. Finally, we show that an s-t-flow that is optimal with respect to the average latency objective is near optimal for the maximum latency objective, and it is close to being fair. Conversely, the average latency of a flow minimizing the maximum latency is also within a constant factor of that of a flow minimizing the average latenc |
| first_indexed | 2024-09-23T16:19:34Z |
| format | Working Paper |
| id | mit-1721.1/5051 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:19:34Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/50512019-04-12T08:22:41Z Computational Complexity, Fairness, and the Price of Anarchy of the Maximum Latency Problem Correa, Jose R. Schulz, Andreas S. Stier Moses, Nicolas E. System Optimum User Equilibrium Selfish Routing Price of Anarchy Approximation Algorithms Multicriteria Optimization Multicommodity Flows We study the problem of minimizing the maximum latency of flows in networks with congestion. We show that this problem is NP-hard, even when all arc latency functions are linear and there is a single source and sink. Still, one can prove that an optimal flow and an equilibrium flow share a desirable property in this situation: all flow-carrying paths have the same length; i.e., these solutions are "fair," which is in general not true for the optimal flow in networks with nonlinear latency functions. In addition, the maximum latency of the Nash equilibrium, which can be computed efficiently, is within a constant factor of that of an optimal solution. That is, the so-called price of anarchy is bounded. In contrast, we present a family of instances that shows that the price of anarchy is unbounded for instances with multiple sources and a single sink, even in networks with linear latencies. Finally, we show that an s-t-flow that is optimal with respect to the average latency objective is near optimal for the maximum latency objective, and it is close to being fair. Conversely, the average latency of a flow minimizing the maximum latency is also within a constant factor of that of a flow minimizing the average latenc 2004-03-05T20:57:38Z 2004-03-05T20:57:38Z 2004-03-05T20:57:38Z Working Paper http://hdl.handle.net/1721.1/5051 en_US MIT Sloan School of Management Working Paper;4447-03 200756 bytes application/pdf application/pdf |
| spellingShingle | System Optimum User Equilibrium Selfish Routing Price of Anarchy Approximation Algorithms Multicriteria Optimization Multicommodity Flows Correa, Jose R. Schulz, Andreas S. Stier Moses, Nicolas E. Computational Complexity, Fairness, and the Price of Anarchy of the Maximum Latency Problem |
| title | Computational Complexity, Fairness, and the Price of Anarchy of the Maximum Latency Problem |
| title_full | Computational Complexity, Fairness, and the Price of Anarchy of the Maximum Latency Problem |
| title_fullStr | Computational Complexity, Fairness, and the Price of Anarchy of the Maximum Latency Problem |
| title_full_unstemmed | Computational Complexity, Fairness, and the Price of Anarchy of the Maximum Latency Problem |
| title_short | Computational Complexity, Fairness, and the Price of Anarchy of the Maximum Latency Problem |
| title_sort | computational complexity fairness and the price of anarchy of the maximum latency problem |
| topic | System Optimum User Equilibrium Selfish Routing Price of Anarchy Approximation Algorithms Multicriteria Optimization Multicommodity Flows |
| url | http://hdl.handle.net/1721.1/5051 |
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