In this article, we present Approximation Schemes for Capacitated Vehicle Routing Problem (CVRP) on several classes of graphs. CVRP, introduced by Dantzig and Ramser in 1959 [ 14 ], are given a graph G=(V,E) with metric edges costs, depot r ∈ V , vehicle bounded capacity Q . The goal is to find minimum cost collection tours the that returns depot, each visiting at most nodes, such they cover al...

In this talk we study how to route online splittable flows in bidirectional ring networks to minimize maximum load. We show that the competitive ratio of any deterministic online algorithm for this problem is at least 2−2/n, where n is the size of the ring, and that the online algorithm that splits each flow inversely proportionally to the length of the flow’s shortest path achieves this compet...

We analyze 2-terminal routing games with linear cost functions and with unknown number of active players. We deal with both splittable and unsplittable models. We prove the existence and uniqueness of a symmetric safety-level equilibrium in such games and show that in many cases every player benefits from the common ignorance about the number of players. Furthermore, we prove new theorems on ex...

A graph embedded in the 3-sphere is called irreducible if it is non-splittable and for any 2-sphere embedded in the 3-sphere that intersects the graph at one point the graph is contained in one of the 3-balls bounded by the 2-sphere. We show that irreducibility is preserved under certain deformations of embedded graphs. We show that certain embedded graphs are irreducible. 2000 Mathematics Subj...

Pseudo-random number generation is a fundamental problem in computer programming. In the case of sequential processing the problem is very well researched, but parallel processing raises new problems whereof far too little is currently understood. Splittable pseudo-random generators (S-PRNG) have been proposed to meet the challenges of parallelism. While applicable to any programming paradigm, ...

A very well–covered graph is an unmixed without isolated vertices such that the height of its edge ideal half number vertices. We study these graphs by means Betti splittings and mapping cone constructions. show cover ideals Cohen–Macaulay are splittable. As a consequence, we compute explicitly minimal graded free resolution class prove have homological linear quotients. Finally, conjecture sam...

We present novel oblivious routing algorithms for both splittable and unsplittable multicommodity flow. Our algorithm for minimizing congestion for unsplittable multicommodity flow is the first oblivious routing algorithm for this setting. As an intermediate step towards this algorithm, we present a novel generalization of Valiant’s classical load balancing scheme for packet-switched networks t...

The Robust Network Loading Problem (RNL) can be stated as follows. Given a graph and a set of traffic matrices, install minimum cost integer capacities on the edges such that all the matrices can be routed non simultaneously on the network. The routing scheme is said to be dynamic if we can choose a (possibly) different routing for every matrix, it is called static if the routing must be the sa...