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In computer networks, participants may cooperate in processing tasks, so thatloads are balanced among them. We present local distributed algorithms that(repeatedly) use local imbalance criteria to transfer loads concurrently acrossthe participants of the system, iterating until all loads are balanced. Ouralgorithms are based on a short local deal-agreement communication ofproposal/deal, based on the neighborhood loads. They converge monotonically,always providing a better state as the execution progresses. Besides, ouralgorithms avoid making loads temporarily negative. Thus, they may beconsidered anytime ones, in the sense that they can be stopped at any timeduring the execution. We show that our synchronous load balancing algorithmsachieve $\epsilon$-Balanced state for the continuous setting and 1-Balancedstate for the discrete setting in all graphs, within $O(n D \log(nK/\epsilon))$ and $O(n D \log(n K/D) + n D^2)$ time, respectively, where $n$ isthe number of nodes, $K$ is the initial discrepancy, $D$ is the graph diameter,and $\epsilon$ is the final discrepancy. Our other monotonic synchronous andasynchronous algorithms for the discrete setting are generalizations of thefirst presented algorithms, where load balancing is performed concurrently withmore than one neighbor. These algorithms arrive at a 1-Balanced state in time$O(n K^2)$ in general graphs, but have a potential to be faster as the loadsare balanced among all neighbors, rather than with only one; we describe ascenario that demonstrates the potential for a fast ($O(1)$) convergence. Ourasynchronous algorithm avoids the need to wait for the slowest participants'activity prior to making the next load balancing steps as synchronous settingsrestrict. We also introduce a self-stabilizing version of our asynchronousalgorithm.

Local Deal-Agreement Based Monotonic Distributed Algorithms for Load Balancing in General Graphs