Routing Symmetric Demands in Directed Minor-Free Graphs with Constant Congestion

The problem of routing in graphs using node-disjoint paths has received a lot of attention and a polylogarithmic approximation algorithm with constant congestion is known for undirected graphs [Chuzhoy and Li 2016] and [Chekuri and Ene 2013]. However, the problem is hard to approximate within polynomial factors on directed graphs, for any constant congestion [Chuzhoy, Kim and Li 2016]. Recently, [Chekuri, Ene and Pilipczuk 2016] have obtained a polylogarithmic approximation with constant congestion on directed planar graphs, for the special case of symmetric demands. We extend their result by obtaining a polylogarithmic approximation with constant congestion on arbitrary directed minor-free graphs, for the case of symmetric demands

Improved Bi-criteria Approximation for the All-or-Nothing Multicommodity Flow Problem in Arbitrary Networks

This paper addresses the following fundamental maximum throughput routing problem: Given an arbitrary edge-capacitated $n$-node directed network and a set of $k$ commodities, with source-destination pairs $(s_i,t_i)$ and demands $d_i> 0$, admit and route the largest possible number of commodities -- i.e., the maximum {\em throughput} -- to satisfy their demands. The main contributions of this paper are two-fold: First, we present a bi-criteria approximation algorithm for this all-or-nothing multicommodity flow (ANF) problem. Our algorithm is the first to achieve a {\em constant approximation of the maximum throughput} with an {\em edge capacity violation ratio that is at most logarithmic in $n$}, with high probability. Our approach is based on a version of randomized rounding that keeps splittable flows, rather than approximating those via a non-splittable path for each commodity: This allows our approach to work for {\em arbitrary directed edge-capacitated graphs}, unlike most of the prior work on the ANF problem. Our algorithm also works if we consider the weighted throughput, where the benefit gained by fully satisfying the demand for commodity $i$ is determined by a given weight $w_i>0$. Second, we present a derandomization of our algorithm that maintains the same approximation bounds, using novel pessimistic estimators for Bernstein's inequality. In addition, we show how our framework can be adapted to achieve a polylogarithmic fraction of the maximum throughput while maintaining a constant edge capacity violation, if the network capacity is large enough. One important aspect of our randomized and derandomized algorithms is their {\em simplicity}, which lends to efficient implementations in practice

Constant Congestion Routing of Symmetric Demands in Planar Directed Graphs

We study the problem of routing symmetric demand pairs in planar digraphs. The input consists of a directed planar graph G = (V, E) and a collection of k source-destination pairs M = {s_1t_1, ..., s_kt_k}. The goal is to maximize the number of pairs that are routed along disjoint paths. A pair s_it_i is routed in the symmetric setting if there is a directed path connecting s_i to t_i and a directed path connecting t_i to s_i. In this paper we obtain a randomized poly-logarithmic approximation with constant congestion for this problem in planar digraphs. The main technical contribution is to show that a planar digraph with directed treewidth h contains a constant congestion crossbar of size Omega(h/polylog(h))

A Comparison of System Optimal and User Optimal Route Guidance.

The work described in this paper (carried out under the EC `DRIVE' programme) extends the simulations described in Working Paper 315, with the aim of studying the likely benefits to and reactions of drivers to system optimal (SO) route guidance - in particular, these effects are compared with those obtained under user optimal (UE) guidance. The model used is again one of a multiple user class equilibrium assignment, so that equipped drivers may be directed to more than one route per origin-destination movement. UE and SO guidance are compared, at different levels of equipped vehicles and demand levels, on the basis of the number of routes they recommend and the similarity of the flows on these routes, as well as link-based properties such as actual flows and queues resulting. These serve to demonstrate the extent to which the routes recommended under UE guidance serve as proxies to those under SO guidance. Secondly, a comparison is made of average (dis)benefits to guided drivers as well as the excess travel time incurred by individual equipped drivers in following SO, as opposed to UE guidance, in order to determine the extent of user sub-optimality of SO routing. Thirdly, input from a parallel DRIVE project, investigating user reactions to guidance information, is used to infer the extent to which drivers are likely to accept the sub-optimality of SO guidance, and the factors which are likely to influence their acceptance. Finally, some preliminary analysis is performed on combined strategies, which aim to strike a balance between the system benefits of SO guidance and the user benefits of UE routing

A Comparison of System Optimal and User Optimal Route Guidance.

The work described in this paper (carried out under the EC `DRIVE' programme) extends the simulations described in Working Paper 315, with the aim of studying the likely benefits to and reactions of drivers to system optimal (SO) route guidance - in particular, these effects are compared with those obtained under user optimal (UE) guidance. The model used is again one of a multiple user class equilibrium assignment, so that equipped drivers may be directed to more than one route per origin-destination movement. UE and SO guidance are compared, at different levels of equipped vehicles and demand levels, on the basis of the number of routes they recommend and the similarity of the flows on these routes, as well as link-based properties such as actual flows and queues resulting. These serve to demonstrate the extent to which the routes recommended under UE guidance serve as proxies to those under SO guidance. Secondly, a comparison is made of average (dis)benefits to guided drivers as well as the excess travel time incurred by individual equipped drivers in following SO, as opposed to UE guidance, in order to determine the extent of user sub-optimality of SO routing. Thirdly, input from a parallel DRIVE project, investigating user reactions to guidance information, is used to infer the extent to which drivers are likely to accept the sub-optimality of SO guidance, and the factors which are likely to influence their acceptance. Finally, some preliminary analysis is performed on combined strategies, which aim to strike a balance between the system benefits of SO guidance and the user benefits of UE routing