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Vertex Coloring with Communication Constraints in Synchronous Broadcast Networks

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This paper considers distributed vertex-coloring in broadcast/receive networks suffering from conflicts and collisions. (A collision occurs when, during the same round, messages are sent to the same process by too… Click to show full abstract

This paper considers distributed vertex-coloring in broadcast/receive networks suffering from conflicts and collisions. (A collision occurs when, during the same round, messages are sent to the same process by too many neighbors; a conflict occurs when a process and one of its neighbors broadcast during the same round.) More specifically, the paper focuses on multi-channel networks, in which a process may either broadcast a message to its neighbors or receive a message from at most $\gamma$γ of them. The paper first provides a new upper bound on the corresponding graph coloring problem (known as frugal coloring) in general graphs, proposes an exact bound for the problem in trees, and presents a deterministic, parallel, color-optimal, collision- and conflict-free distributed coloring algorithm for trees, and proves its correctness.

Keywords: broadcast; constraints synchronous; vertex coloring; coloring communication; communication constraints; synchronous broadcast

Journal Title: IEEE Transactions on Parallel and Distributed Systems
Year Published: 2019

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