Parallel Load Balancing on constrained client-server topologies

We study parallel Load Balancing protocols for the client-server distributed model defined as follows. There is a set C of n clients and S servers where each client has (at most) constant number d⩾1 requests that must be assigned to some server. The server one are connected other via fixed bipartite graph: v can only sent in its neighborhood N(v). goal assign every request so minimize maximum load servers. In this setting, efficient available dense topologies. particular, simple protocol, named raes, been recently introduced by Becchetti et al. [1] regular graphs. They show symmetric, non-adaptive protocol achieves with completion time O(log⁡n) overall work O(n), w.h.p. Motivated proximity constraints arising systems, we analyze raes over almost-regular graphs nodes may have neighborhoods small size. detail, prove that, w.h.p., keeps same performances above (in terms load, time, complexity, respectively) on any graph degree Ω(log2⁡n). Our analysis significantly departs from since it requires cope non-trivial stochastic-dependence issues random choices algorithmic process which due worst-case, sparse topology underlying graph.