The notion of a split coloring of a complete graph was introduced by Erdős and Gyárfás [7] as a generalization of split graphs. In this paper, we offer an alternate interpretation by comparing such a coloring to the classical Ramsey coloring problem via a two-round game played against an adversary. We show that the techniques used and bounds obtained on the extremal (r,m)-split coloring problem...

We devise a new approximation algorithm for capacitated vehicle routing. Our yields better ratio general routing as well the unit-demand case and splittable variant. results hold in arbitrary metric spaces. This is first improvement on classical tour partitioning by Haimovich Rinnooy Kan [16] Altinkemer Gavish [2].

The two-dimensional knapsack problem consists in packing rectangular items into a single box such that the total value of packed is maximized. In this article, we restrict to 2-stage non-exact guillotine cut packings and consider variant with splittable items: each item can be horizontally as many times needed, may contain only portion an item. This arises semifluid items, like tubes small radi...

In traditional multi-commodity flow theory, the task is to send a certain amount of each commodity from its start to its target node, subject to capacity constraints on the edges. However, no restriction is imposed on the number of paths used for delivering each commodity; it is thus feasible to spread the flow over a large number of different paths. Motivated by routing problems arising in rea...

Motivated by a famous open question on the single-source unsplittable minimum cost flow problem, we present a new approximation result for the relaxation of the problem where, for a given number k, each commodity must be routed along at most k paths. © 2009 Elsevier B.V. All rights reserved.

Classical network flow problems do not impose restrictions on the choice of paths on which flow is sent. Only the arc capacities of the network have to be obeyed. This scenario is not always realistic. In fact, there are many problems for which, e.g., the number of paths being used to route a commodity or the length of such paths has to be small. These restrictions are considered in the length-...