10 research outputs found
LP-based Covering Games with Low Price of Anarchy
We present a new class of vertex cover and set cover games. The price of
anarchy bounds match the best known constant factor approximation guarantees
for the centralized optimization problems for linear and also for submodular
costs -- in contrast to all previously studied covering games, where the price
of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In
particular, we describe a vertex cover game with a price of anarchy of 2. The
rules of the games capture the structure of the linear programming relaxations
of the underlying optimization problems, and our bounds are established by
analyzing these relaxations. Furthermore, for linear costs we exhibit linear
time best response dynamics that converge to these almost optimal Nash
equilibria. These dynamics mimic the classical greedy approximation algorithm
of Bar-Yehuda and Even [3]
Distributed and Parallel Algorithms for Set Cover Problems with Small Neighborhood Covers
In this paper, we study a class of set cover problems that satisfy a special
property which we call the {\em small neighborhood cover} property. This class
encompasses several well-studied problems including vertex cover, interval
cover, bag interval cover and tree cover. We design unified distributed and
parallel algorithms that can handle any set cover problem falling under the
above framework and yield constant factor approximations. These algorithms run
in polylogarithmic communication rounds in the distributed setting and are in
NC, in the parallel setting.Comment: Full version of FSTTCS'13 pape
Identifying the parametric occurrence of multiple steady states for some biological networks
We consider a problem from biological network analysis of determining regions
in a parameter space over which there are multiple steady states for positive
real values of variables and parameters. We describe multiple approaches to
address the problem using tools from Symbolic Computation. We describe how
progress was made to achieve semi-algebraic descriptions of the
multistationarity regions of parameter space, and compare symbolic results to
numerical methods. The biological networks studied are models of the
mitogen-activated protein kinases (MAPK) network which has already consumed
considerable effort using special insights into its structure of corresponding
models. Our main example is a model with 11 equations in 11 variables and 19
parameters, 3 of which are of interest for symbolic treatment. The model also
imposes positivity conditions on all variables and parameters.
We apply combinations of symbolic computation methods designed for mixed
equality/inequality systems, specifically virtual substitution, lazy real
triangularization and cylindrical algebraic decomposition, as well as a
simplification technique adapted from Gaussian elimination and graph theory. We
are able to determine multistationarity of our main example over a
2-dimensional parameter space. We also study a second MAPK model and a symbolic
grid sampling technique which can locate such regions in 3-dimensional
parameter space.Comment: 60 pages - author preprint. Accepted in the Journal of Symbolic
Computatio
Distributed Weighted Vertex Cover via Maximal Matchings
In this paper we consider the problem of computing a minimumweight vertex-cover in an n-node, weighted, undirected graph G = (V,E). We present a fully distributed algorithm for computing vertex covers of weight at most twice the optimum, in the case of integer weights. Our algorithm runs in an expected number of O(logn + log ˆW) communication rounds, where ˆW is the average vertex-weight. The previous best algorithm for this problem requires O(logn(logn + log ˆW)) rounds and it is not fully distributed. For a maximal matching M in G it is a well-known fact that any vertex-cover in G needs to have at least |M | vertices. Our algorithm is based on a generalization of this combinatorial lower-bound to the weighted setting
Distributed weighted vertex cover via maximal matchings
In this article, we consider the problem of computing a minimum-weight vertex-cover in an n-node, weighted, undirected graph G = (V,E). We present a fully distributed algorithm for computing vertex covers of weight at most twice the optimum, in the case of integer weights. Our algorithm runs in an expected number of O(log n + log Ŵ) communication rounds, where Ŵ is the average vertex-weight. The previous best algorithm for this problem requires O(log n(log n + logŴ)) rounds and it is not fully distributed. For a maximal matching M in G, it is a well-known fact that any vertex-cover in G needs to have at least M vertices. Our algorithm is based on a generalization of this combinatorial lower-bound to the weighted setting. © 2008 ACM
Algorithmes d'approximation à mémoire limitée pour le traitement de grands graphes (le problème du Vertex Cover)
Nous nous sommes intéressés à un problème d'optimisation sur des graphes (le problème du Vertex Cover) dans un contexte bien particulier : celui des grandes instances de données. Nous avons défini un modèle de traitement se basant sur trois contraintes (en relation avec la quantité de mémoire limitée, par rapport à la grande masse de données à traiter) et qui reprenait des propriétés issus de plusieurs modèles existants. Nous avons étudié plusieurs algorithmes adaptés à ce modèle. Nous avons analysé, tout d'abord de façon théorique, la qualité de leurs solutions ainsi que leurs complexités. Nous avons ensuite mené une étude expérimentale sur de gros graphes. De manière générale, les travaux menés durant cette thèse peuvent fournir des indicateurs pour choisir le ou les algorithmes qui conviennent le mieux pour traiter le problème du vertex cover sur de gros graphes. Choisir un algorithme (qui plus est d'approximation) qui soit à la foisperformant (en terme de qualité de solution et de complexité) et qui satisfasse les contraintes du modèle que l'on considère est délicat. en effet, les algorithmes les plus performants ne sont pas toujours les mieux adaptés. dans les travaux que nous avons réalisés, nous sommes parvenus à la conclusion qu'il est préférable de choisir au départ l'algorithme qui est le mieux adapté plutôt que de choisir celui qui est le plus performant.We are interested to an optimization problem on graphs (the Vertex Cover problem) in a very specific context : the huge instances of data. We defined a treatment model based on three constraints (in connection with the limited amount of memory compared to the huge amount of data to be processed) and that reproduces properties from several existing models. We studied several algorithms adapted to this model. We examined, first theoretically, their solutions quality and their complexities. We then conducted an experimental study on large graphs. In general, the work made during this thesis may provide indicators for select algorithms that are best suited to resolve the Vertex Cover problem on large graphs. Choose an algorithm (which is approximated) that is both efficient (in terms of quality of solution and complexity) and satisfies the constraints model whether we consider is tricky. in fact, the most efficient algorithms are not always the best adapted. In the work we have done, we reached the conclusion that, at the beginning, it is best to choose the best suited algorithm rather than the more efficient.EVRY-Bib. électronique (912289901) / SudocSudocFranceF