Round weighting problem and gathering in radio networks with symmetrical interference

Abstract

International audienceIn this article we consider the problem of gathering information in a gateway in a radio mesh access network. Due to interferences, calls (transmissions) cannot be performed simultaneously. This leads us to define a round as a set of non-interfering calls. Following the work of Klasing, Morales and Pérennes, we model the problem as a Round Weighting Problem (RWP) in which the objective is to minimize the overall period of non-interfering calls activations (total number of rounds) providing enough capacity to satisfy the throughput demand of the nodes.We develop tools to obtain lower and upper bounds for general graphs. Then, more precise results are obtained considering a symmetric interference model based on distance of graphs, called the distance-d interference model (the particular case d= 1 corresponds to the primary node model).We apply the presented tools to get lower bounds for grids with thegateway either in the middle or in the corner. We obtain upper boundswhich in most of the cases match the lower bounds, using strategiesthat either route the demand of a single node or route simultaneously flow from several source nodes. Therefore, weobtain exact and constructive results for grids, in particularfor the case of uniform demands answering a problem asked by Klasing, Morales and Pérennes

On the complexity of the flow coloring problem

“…The remaining (even) demand b v ℓ − δ of v ℓ is sent by one iteration of loop 8-12 with this amount of colors. Therefore, inequality (3) …”

“…The FCP d as defined in Section 1 is studied by Bermond, Huiban and Reyes [3] and Huiban [8], as a variant of the RWP. Tools for obtaining lower and upper bounds as well as a d+1 ⌈ d+1 2 ⌉ -approximation algorithm are developed.…”