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- Bilel Derbel, El-Ghazali Talbi
- 2010 IEEE 30th International Conference on…
- 2010

Given a palette $P$ of at most $\xi$ colors, and a parameter $d$, a $(d,\xi)$-coloring of a graph is an assignment of a color from the palette $P$ to every node in the graph such that any two nodes at distance at most $d$ have different colors. We prove that for every $n$-node unit disk graph with maximum degree $\Delta$, there exists a distributed… (More)

- Bilel Derbel, Mohamed Mosbah, Akka Zemmari
- Theory of Computing Systems
- 2009

We present new efficient deterministic and randomized distributed algorithms for decomposing a graph with n nodes into a disjoint set of connected clusters with radius at most k−1 and having O(n 1+1/k ) intercluster edges. We show how to implement our algorithms in the distributed $\mathcal{CONGEST}$ model of computation, i.e., limited message size, which… (More)

- Bilel Derbel, Cyril Gavoille, David Peleg, Laurent Viennot
- PODC
- 2008

The paper presents a deterministic distributed algorithm that, given k ≥ 1, constructs in k rounds a (2k-1,0)-spanner of O(k n<sup>1+1/k</sup>) edges for every n-node unweighted graph. (If n is not available to the nodes, then our algorithm executes in 3k-2 rounds, and still returns a (2k-1,0)-spanner with O(k n<sup>1+1/k</sup>) edges.) Previous… (More)

- Bilel Derbel, Mohamed Mosbah, Akka Zemmari
- Proceedings 20th IEEE International Parallel…
- 2006

This paper presents efficient deterministic and randomized distributed algorithms for decomposing a graph with n nodes into a disjoint set of connected clusters with small radius and few intercluster edges. Our algorithms can be easily implemented in the distributed CONGEST model of computation i.e., limited message size, improving the time complexity of… (More)

- Bilel Derbel, El-Ghazali Talbi
- ICDCN
- 2010

The paper deals with radio network distributed algorithms where nodes are not aware of their one hop neighborhood. Given an n-node graph modeling a multihop network of radio devices, we give a O(log 2 n) time distributed algorithm that computes w.h.p., a constant approximation value of the degree of each node. We also provide a O(∆ log n + log 2 n) time… (More)

- Bilel Derbel, Cyril Gavoille
- SIROCCO
- 2006

This paper concerns the efficient construction of sparse and low stretch spanners for unweighted arbitrary graphs with n nodes. All previous deterministic distributed algorithms, for constant stretch spanners of o(n 2) edges, have a running time Ω (n) for some constant > 0 depending on the stretch. Our deterministic distributed algorithms construct constant… (More)

- Bilel Derbel, Cyril Gavoille, David Peleg
- DISC
- 2007

The paper presents a deterministic distributed algorithm that given an n node unweighted graph constructs an O(n 3/2) edge 3-spanner for it in O(log n) time. This algorithm is then extended into a de-terministic algorithm for computing an O(k n 1+1/k) edge O(k)-spanner in 2 O(k) log k−1 n time for every integer parameter k 1. This establishes that the… (More)

Recently, there has been a renewed interest in decomposition-based approaches for evolutionary multiobjective optimization. However, the impact of the choice of the underlying scalarizing function(s) is still far from being well understood. In this paper, we investigate the behavior of different scalarizing functions and their parameters. We thereby… (More)

- Thanh-Do Tran, Dimo Brockhoff, Bilel Derbel
- GECCO
- 2013

The idea of multiobjectivization is to reformulate a single-objective problem as a multiobjective one. In one of the scarce studies proposing this idea for problems in <i>continuous</i> domains, the distance to the closest neighbor (DCN) in the population of a multiobjective algorithm has been used as the additional (dynamic) second objective. As no… (More)

- Bilel Derbel, Mohamed Mosbah
- IV
- 2003