Vertex Coloring with Communication Constraints in Synchronous Broadcast Networks

Hicham Lakhlef (1) , Michel Raynal (2) , François Taïani (2)

1 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
2 WIDE - the World Is Distributed Exploring the tension between scale and coordination

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 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; presents a deterministic, parallel, color-optimal, collision-and conflict-free distributed coloring algorithm for trees; proves the correctness of this algorithm; and finally evaluates experimentally its performance using simulations that show our solution clearly outperforms a reference protocol for distributed TDMA slot-allocation.

Mots clés: Vertex coloring; TDMA slot allocation !; Index Terms-Distributed algorithms; Message-passing; Broadcast/receive communication; Synchronous systems; Multi-coloring

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

Hicham Lakhlef, Michel Raynal, François Taïani. Vertex Coloring with Communication Constraints in Synchronous Broadcast Networks. IEEE Transactions on Parallel and Distributed Systems, 2019, 30 (7), pp.1672-1686. ⟨10.1109/TPDS.2018.2889688⟩. ⟨hal-02376726⟩