Continuum Equilibria and Global Optimization for Routing in Dense Static Ad Hoc Networks

We consider massively dense ad hoc networks and study their continuum limits as the node density increases and as the graph providing the available routes becomes a continuous area with location and congestion dependent costs. We study both the global optimal solution as well as the non-cooperative routing problem among a large population of users where each user seeks a path from its origin to its destination so as to minimize its individual cost. Finally, we seek for a (continuum version of the) Wardrop equilibrium. We first show how to derive meaningful cost models as a function of the scaling properties of the capacity of the network and of the density of nodes. We present various solution methodologies for the problem: (1) the viscosity solution of the Hamilton-Jacobi-Bellman equation, for the global optimization problem, (2) a method based on Green's Theorem for the least cost problem of an individual, and (3) a solution of the Wardrop equilibrium problem using a transformation into an equivalent global optimization problem

Design and analysis of a beacon-less routing protocol for large volume content dissemination in vehicular ad hoc networks

Largevolumecontentdisseminationispursuedbythegrowingnumberofhighquality applications for Vehicular Ad hoc NETworks(VANETs), e.g., the live road surveillance service and the video-based overtaking assistant service. For the highly dynamical vehicular network topology, beacon-less routing protocols have been proven to be efficient in achieving a balance between the system performance and the control overhead. However, to the authors’ best knowledge, the routing design for large volume content has not been well considered in the previous work, which will introduce new challenges, e.g., the enhanced connectivity requirement for a radio link. In this paper, a link Lifetime-aware Beacon-less Routing Protocol (LBRP) is designed for large volume content delivery in VANETs. Each vehicle makes the forwarding decision based on the message header information and its current state, including the speed and position information. A semi-Markov process analytical model is proposed to evaluate the expected delay in constructing one routing path for LBRP. Simulations show that the proposed LBRP scheme outperforms the traditional dissemination protocols in providing a low end-to-end delay. The analytical model is shown to exhibit a good match on the delay estimation with Monte Carlo simulations, as well

Setting Parameters by Example

We introduce a class of "inverse parametric optimization" problems, in which one is given both a parametric optimization problem and a desired optimal solution; the task is to determine parameter values that lead to the given solution. We describe algorithms for solving such problems for minimum spanning trees, shortest paths, and other "optimal subgraph" problems, and discuss applications in multicast routing, vehicle path planning, resource allocation, and board game programming.Comment: 13 pages, 3 figures. To be presented at 40th IEEE Symp. Foundations of Computer Science (FOCS '99