Input-dynamic distributed graph algorithms for congested networks
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Consider a distributed system, where the topology of the communication network remains fixed, but local inputs given to nodes may change over time. In this work, we explore the following question: if some of the local inputs change, can an existing solution be updated efficiently, in a dynamic and distributed manner? To address this question, we define the batch dynamic CONGEST model, where the communication network G = (V,E) remains fixed and a dynamic edge labelling defines the problem input. The task is to maintain a solution to a graph problem on the labeled graph under batch changes. We investigate, when a batch of α edge label changes arrive, – how much time as a function of α we need to update an existing solution, and – how much information the nodes have to keep in local memory between batches in order to update the solution quickly. We give a general picture of the complexity landscape in this model, including a general framework for lower bounds. In particular, we prove non-trivial upper bounds for two selected, contrasting problems: maintaining a minimum spanning tree and detecting cliques.
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