Mohamed Mosbah

Monadic second-order evaluations on tree-decomposable graphs

Abstract Every graph generated by a hyperedge replacement graph-grammar can be represented by a tree, namely the derivation tree of the derivation sequence that produced it. Certain functions on graphs can be computed recursively on the derivation trees of these graphs. By using monadic second-order logic and semiring homomorphisms, we describe in a single formalism a large class of such functions. Polynomial and even linear algorithms can be constructed for some of these functions. We unify similar results obtained by Takamizawa (1982), Bern (1987), Arnborg (1991) and Habel (1989).

Convex Drawings of 3-Connected Plane Graphs

AbstractWe use Schnyder woods of 3-connected planar graphs to produce convex straight-line drawings on a grid of size

Wagner's Theorem on Realizers

(n-2-\Delta)\times (n-2-\Delta).

Convex drawings of 3-connected plane graphs

The parameter

Fast and Secure Multihop Broadcast Solutions for Intervehicular Communication

\Delta\geq 0

Electing a leader in the local computation model using mobile agents

depends on the Schnyder wood used for the drawing. This parameter is in the range

A Synchronous Tiered Based Clustering Algorithm for large-scale Ad hoc Networks

0 \leq \Delta\leq {n}/{2}-2.

Watermelon uniform random generation with applications

The algorithm is a refinement of the face-counting algorithm; thus, in particular, the size of the grid is at most

A Unified Framework for Designing, Implementing and Visualizing Distributed Algorithms

(f-2)\times(f-2).

Distributed Computation of a Spanning Tree in a Dynamic Graph by Mobile Agents

The above bound on the grid size simultaneously matches or improves all previously known bounds for convex drawings, in particular Schnyders and the recent Zhang and He bound for triangulations and the Chrobak and Kant bound for 3-connected planar graphs. The algorithm takes linear time. The drawing algorithm has been implemented and tested. The expected grid size for the drawing of a random triangulation is close to