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Integer traffic assignment problem: Algorithms and insights on random graphs.

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Area of Science:

  • Operations Research
  • Computer Science
  • Network Optimization

Background:

  • Path optimization is crucial for real-world systems like traffic and data routing.
  • The traffic assignment problem (TAP) is a continuous optimization problem.
  • The integer traffic assignment problem (ITAP) is a discrete, NP-hard variant of TAP.

Purpose of the Study:

  • To develop and evaluate algorithms for solving the integer traffic assignment problem (ITAP).
  • To explore both repulsive (congestion minimization) and attractive (edge usage minimization) interaction scenarios.
  • To analyze the relationship and convergence between TAP and ITAP.

Main Methods:

  • Implemented and compared four algorithms: message passing, greedy approach, simulated annealing, and relaxation to TAP.
  • Conducted experiments on large sparse random regular graphs with random origin-destination pairs.
  • Investigated scaling regimes and convergence rates between TAP and ITAP solutions.

Main Results:

  • The greedy algorithm is competitive in repulsive scenarios.
  • Message passing and simulated annealing show superior performance in attractive scenarios.
  • The solution of TAP converges to ITAP as the number of paths increases, with identified scaling regimes.

Conclusions:

  • Different algorithms are effective for ITAP depending on the interaction type (repulsive vs. attractive).
  • The continuous TAP provides a close approximation to ITAP under specific conditions (large number of paths).
  • Understanding the TAP-ITAP relationship is key for efficient network flow optimization.