# Contribution à l'algorithmique distribuée : arbres et ordonnancement

Abstract : In this "Licence to supervise research" (HDR in French) thesis, we present a study of distributed asynchronous algorithms for control and scheduling. A control algorithm establishes a virtual structure over a network of communicating sites. We choose to make a minimum of assumptions about the knowledge of each site. In this study, we only consider networks of sites sharing neither memory nor global clock. Sites work in parallel, asynchronously and each computation is only performed by message exchange. In such a context, distributed algorithms are called ''message-driven''. We try to limit waiting states by not introducing synchronization mechanisms. Generally speaking, we make no particular assumption on the way algorithms start, namely, any non-empty subset of sites may start an algorithm. We try to remain as general as possible but in this work, we limit our considerations to deterministic algorithms. Our assumptions are supporting the essential properties of distributed algorithms~: that is essentially the local behavior. A control algorithm establishes a virtual structure over the whole network in which each site can distinguish some of its neighbors to play special roles. More particularly, we have chosen to study structures which are similar to trees. We recall that numerous problems in distributed computing, such as distributed termination and leader election, can be reduced to spanning tree construction. In order to construct such a structure or to elect a leader, most of known distributed algorithms transform this problem into an extrema-finding problem. In fact, they elect the site which has the greatest (or the lowest) identity and construct a spanning tree at the same time. In a first part, we study algorithms to construct constrained spanning trees, these constraints contribute to a greater efficiency to the control structure established. The most popular constraint is the minimum total weight, which represents an economical criterion. To our knowledge, the Minimum Diameter Spanning Tree is a problem which had never been addressed in the field of distributed research. We consider ''weighted'' diameter~: viz. the diameter $D$ of a graph is the sum of the edges' weights along the longest shortest path. If we consider time complexity, this constraint is obviously of great interest, since it always exists a couple of sites needing at least $D$ units of time to exchange information. The Minimum Degree Spanning Tree is a new problem in the field of distributed research also. This constraint allows, for example, the use of cheaper interconnection equipments. We present an approximate algorithm for this problem (proven to be NP-hard) that find a spanning tree of degree 1 to the optimum. In the final part we are interested in finding efficient heuristics to the problem of distributed on-line scheduling, with sporadic arrivals, first for independent tasks and next for tasks with dependencies (directed acyclic graph of dependencies). We show that the tree structure can be used with much benefits. In particular, in arbitrary wide networks, shortest paths trees limited to not too far neighbors can be used to define a new and promising concept: the computing sphere. This computing sphere limits exchanged messages and computation time.
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Document type :
Habilitation à diriger des recherches

Cited literature [11 references]

https://tel.archives-ouvertes.fr/tel-00595915
Contributor : Franck Butelle <>
Submitted on : Wednesday, May 25, 2011 - 10:13:14 PM
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• HAL Id : tel-00595915, version 1

### Citation

Franck Butelle. Contribution à l'algorithmique distribuée : arbres et ordonnancement. Réseaux et télécommunications [cs.NI]. Université Paris-Nord - Paris XIII, 2007. ⟨tel-00595915⟩

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