Jordi Petit

A survey of graph layout problems

Graph layout problems are a particular class of combinatorial optimization problems whose goal is to find a linear layout of an input graph in such way that a certain objective cost is optimized. This survey considers their motivation, complexity, approximation properties, upper and lower bounds, heuristics and probabilistic analysis on random graphs. The result is a complete view of the current state of the art with respect to layout problems from an algorithmic point of view.

MALLBA: a library of skeletons for combinatorial optimisation

The MALLBA project tackles the resolution of combinatorial optimization problems using algorithmic skeletons implemented in C++. mallba offers three families of generic resolution methods: exact, heuristic and hybrid. Moreover, for each resolution method, MALLBA provides three different implementations: sequential, parallel for local area networks, and parallel for wide area networks (currently under development). This paper explains the architecture of the MALLBA library, presents some of its skeletons, and offers several computational results to show the viability of the approach.

Approximating Layout Problems on Random Geometric Graphs

In this paper, we study the approximability of several layout problems on a family of random geometric graphs. Vertices of random geometric graphs are randomly distributed on the unit square and are connected by edges whenever they are closer than some given parameter. The layout problems that we consider are bandwidth, minimum linear arrangement, minimum cut width, minimum sum cut, vertex separation, and edge bisection. We first prove that some of these problems remain NP-complete even for geometric graphs. Afterwards, we compute lower bounds that hold, almost surely, for random geometric graphs. Then, we present two heuristics that, almost surely, turn out to be constant approximation algorithms for our layout problems on random geometric graphs. In fact, for the bandwidth and vertex separation problems, these heuristics are asymptotically optimal. Finally, we use the theoretical results in order to empirically compare these and other well-known heuristics.

Efficient parallel LAN/WAN algorithms for optimization: the MALLBA project

The MALLBA project tackles the resolution of combinatorial optimization problems using generic algorithmic skeletons implemented in C++. A skeleton in the MALLBA library implements an optimization method in one of the three families of generic optimization techniques offered: exact, heuristic and hybrid. Moreover, for each of those methods, MALLBA provides three different implementations: sequential, parallel for Local Area Networks, and parallel for Wide Area Networks. This paper introduces the architecture of the MALLBA library, details some of the implemented skeletons, and offers computational results for some classical optimization problems to show the viability of our library. Among other conclusions, we claim that the design used to develop the optimization techniques included in the library is generic and efficient at the same time.

A random graph model for optical networks of sensors

The main contribution of this paper is presenting a new model for Smart Dust networks communicating through optical links and showing its applicability when the goal of the network is monitoring an area under the surveillance of a base station. We analyze the basic parameters of these networks as a new model of random graphs and propose simple distributed protocols for basic communication. These protocols are designed to minimize the energy consumption.

Convergence Theorems for Some Layout Measures on Random Lattice and Random Geometric Graphs

This work deals with convergence theorems and bounds on the cost of several layout measures for lattice graphs, random lattice graphs and sparse random geometric graphs. Specifically, we consider the following problems: Minimum Linear Arrangement, Cutwidth, Sum Cut, Vertex Separation, Edge Bisection and Vertex Bisection. For full square lattices, we give optimal layouts for the problems still open. For arbitrary lattice graphs, we present best possible bounds disregarding a constant factor. We apply percolation theory to the study of lattice graphs in a probabilistic setting. In particular, we deal with the subcritical regime that this class of graphs exhibits and characterize the behaviour of several layout measures in this space of probability. We extend the results on random lattice graphs to random geometric graphs, which are graphs whose nodes are spread at random in the unit square and whose edges connect pairs of points which are within a given distance. We also characterize the behaviour of several layout measures on random geometric graphs in their subcritical regime. Our main results are convergence theorems that can be viewed as an analogue of the Beardwood, Halton and Hammersley theorem for the Euclidean TSP on random points in the unit square.

Random Geometric Problems on [0, 1]²

In this paper we survey the work done for graphs on random geometric models. We present some heuristics for the problem of the Minimal linear arrangement on [0,1]2 and we conclude with a collection of open problems.

Jutge.org: an educational programming judge

Jutge.org is an open access educational online programming judge where students can try to solve more than 800 problems using 22 programming languages. The verdict of their solutions is computed using exhaustive test sets run under time, memory and security restrictions. By contrast to many popular online judges, Jutge.org is designed for students and instructors: On one hand, the problem repository is mainly aimed to beginners, with a clear organization and gradding. On the other hand, the system is designed as a virtual learning environment where instructors can administer their own courses, manage their roster of students and tutors, add problems, attach documents, create lists of problems, assignments, contests and exams. This paper presents Jutge.org and offers some case studies of courses using it.

COMBINING SPECTRAL SEQUENCING AND PARALLEL SIMULATED ANNEALING FOR THE MINLA PROBLEM

In this paper we present and analyze new sequential and parallel heuristics to approximate the Minimum Linear Arrangement problem (MinLA). The heuristics consist in obtaining a first global solution using Spectral Sequencing and improving it locally through Simulated Annealing. In order to accelerate the annealing process, we present a special neighborhood distribution that tends to favor moves with high probability to be accepted. We show how to make use of this neighborhood to parallelize the Metropolis stage on distributed memory machines by mapping partitions of the input graph to processors and performing moves concurrently. The paper reports the results obtained with this new heuristic when applied to a set of large graphs, including graphs arising from finite elements methods and graphs arising from VLSI applications. Compared to other heuristics, the measurements obtained show that the new heuristic improves the solution quality, decreases the running time and offers an excellent speedup when ran on a commodity network made of nine personal computers.

Efficient and reliable high level communication in randomly deployed wireless sensor networks

In this paper we present a way to establish a reliable and efficient high level communication system in a randomly deployed network of sensors equipped with directional antennas. Such high level communication system will enable the programming of the sensor network using high level communication functionalities without the burden of taking care of their physical capacities (low range, unidirectional links, single frequency, presence of collisions...). The high level communication functionalities we offer include point-to-point communication, point-to-area communication, and one-to-all communication. The basic idea to implement this system is to simulate a virtual network that emerges from the ad-hoc network using self-organization, self-discovery and collaborative methods. The analysis of the protocols we present shows their reasonable efficiency, scalability and robustness.