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- Johanne Cohen, Khaled Maamra, George Manoussakis, Laurence Pilard
- ArXiv
- 2016

Manne et al. [11] designed the first algorithm computing a maximal matching that is a 23 -approximation of the maximum matching in 2 moves. However, the complexity tightness was not proved. In this paper, we exhibit a sub-exponential execution of this matching algorithm : this algorithm can stabilize after at most Ω(2 √ ) moves under the central daemon.

- Johanne Cohen, Khaled Maâmra, George Manoussakis, Laurence Pilard
- ArXiv
- 2016

We present the first polynomial self-stabilizing algorithm for finding a 2 3 -approximation of a maximum matching in a general graph. The previous best known algorithm has been presented by Manne et al. [6] and has a sub-exponential time complexity under the distributed adversarial daemon [1]. Our new algorithm is an adaptation of the Manne et al. algorithm… (More)

- Johanne Cohen, Khaled Maamra, George Manoussakis, Laurence Pilard
- OPODIS
- 2016

We present the first polynomial self-stabilizing algorithm for finding a 3 -approximation of a maximum matching in a general graph. The previous best known algorithm has been presented by Manne et al. [16] and has a sub-exponential time complexity under the distributed adversarial daemon [3]. Our new algorithm is an adaptation of the Manne et al. algorithm… (More)

- Johanne Cohen, George Manoussakis, Laurence Pilard, Devan Sohier
- ArXiv
- 2017

We introduce and study a family of polytopes which can be seen as a generalization of the permutahedron of type Bd. We highlight connections with the largest possible diameter of the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k, and with the computational complexity of multicriteria matroid optimization.

Del Pia and Michini recently improved the upper bound of kd due to Kleinschmidt and Onn for the largest possible diameter of the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k. We introduce Euler polytopes which include a family of lattice polytopes with diameter (k + 1)d/2, and thus reduce the gap between the… (More)

A graph is inductive k-independent if there exists an ordering of its vertices v1, ..., vn such that α(G[N(vi)∩Vi]) ≤ k where N(vi) is the neighbourhood of vi, Vi = {vi, ..., vn} and α is the independence number. In this article we design a polynomial time approximation algorithm with ratio ∆/ log(log(∆)/(k+1)) for the maximum clique problem and also show… (More)

- George Manoussakis
- FCT
- 2017

A graph is k-degenerate if any induced subgraph has a vertex of degree at most k. In this paper we prove new algorithms finding cliques and similar structures in these graphs. We design linear time Fixed-Parameter Tractable algorithms for induced and non induced bicliques. We prove an algorithm listing all maximal bicliques in time O(k(n−k)2), improving the… (More)

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