760 research outputs found
Answer Set Solving with Bounded Treewidth Revisited
Parameterized algorithms are a way to solve hard problems more efficiently,
given that a specific parameter of the input is small. In this paper, we apply
this idea to the field of answer set programming (ASP). To this end, we propose
two kinds of graph representations of programs to exploit their treewidth as a
parameter. Treewidth roughly measures to which extent the internal structure of
a program resembles a tree. Our main contribution is the design of
parameterized dynamic programming algorithms, which run in linear time if the
treewidth and weights of the given program are bounded. Compared to previous
work, our algorithms handle the full syntax of ASP. Finally, we report on an
empirical evaluation that shows good runtime behaviour for benchmark instances
of low treewidth, especially for counting answer sets.Comment: This paper extends and updates a paper that has been presented on the
workshop TAASP'16 (arXiv:1612.07601). We provide a higher detail level, full
proofs and more example
Families with infants: a general approach to solve hard partition problems
We introduce a general approach for solving partition problems where the goal
is to represent a given set as a union (either disjoint or not) of subsets
satisfying certain properties. Many NP-hard problems can be naturally stated as
such partition problems. We show that if one can find a large enough system of
so-called families with infants for a given problem, then this problem can be
solved faster than by a straightforward algorithm. We use this approach to
improve known bounds for several NP-hard problems as well as to simplify the
proofs of several known results.
For the chromatic number problem we present an algorithm with
time and exponential space for graphs of average
degree . This improves the algorithm by Bj\"{o}rklund et al. [Theory Comput.
Syst. 2010] that works for graphs of bounded maximum (as opposed to average)
degree and closes an open problem stated by Cygan and Pilipczuk [ICALP 2013].
For the traveling salesman problem we give an algorithm working in
time and polynomial space for graphs of average
degree . The previously known results of this kind is a polyspace algorithm
by Bj\"{o}rklund et al. [ICALP 2008] for graphs of bounded maximum degree and
an exponential space algorithm for bounded average degree by Cygan and
Pilipczuk [ICALP 2013].
For counting perfect matching in graphs of average degree~ we present an
algorithm with running time and polynomial
space. Recent algorithms of this kind due to Cygan, Pilipczuk [ICALP 2013] and
Izumi, Wadayama [FOCS 2012] (for bipartite graphs only) use exponential space.Comment: 18 pages, a revised version of this paper is available at
http://arxiv.org/abs/1410.220
D-harmonic distributions and global hypoellipticity on nilmanifolds
Let M = Γ\N be a compact nilmanifold. A system of differential operators D1, …, Dk on M is globally hypoelliptic (GH) if when D1f = g1,…, Dkf=gk with f ∈ D’ (M), g1, …, gk ∈ C∞ (M) then f ∈ C∞ (M). Let X1, …, Xk be real vector fields on M induced by the Lie algebra N of N. We study the relationships between (GH) of the system X1, …, Xk on M, (GH) of the operator D = X12 + … + Xk2, the constancy of D-harmonic distributions on M, and related algebraic conditions on X1, …, Xk ∈ N. © 1991 by Pacific Journal of Mathematics
{On Subexponential Running Times for Approximating Directed Steiner Tree and Related Problems}
This paper concerns proving almost tight (super-polynomial) running times, for achieving desired approximation ratios for various problems. To illustrate, the question we study, let us consider the Set-Cover problem with n elements and m sets. Now we specify our goal to approximate Set-Cover to a factor of (1-d)ln n, for a given parameter 0= 2^{n^{c d}}, for some constant 0= exp((1+o(1)){log^{d-c}n}), for any c>0, unless the ETH is false. Our result follows by analyzing the work of Halperin and Krauthgamer [STOC, 2003]. The same lower and upper bounds hold for CST
Formation des prix des légumes à la Réunion. Analyse de la variabilité des prix et des différentiels entre producteurs et consommateurs
Les productions légumières, potentiellement très rémunératrices, sont attractives pour les petits agriculteurs qui cherchent à valoriser davantage leur foncier, toutefois l'ampleur des fluctuations de leur prix entraîne un risque économique important. Outre l'instabilité des prix à court terme, les producteurs sont également préoccupés par l'évolution de leurs rapports commerciaux avec la distribution qui est dans une phase de concentration accélérée. Cette étude apporte un éclairage sur les conditions de formation des prix en abordant deux aspects. D'une part les fluctuations des prix au producteur, caractérisées en distinguant leurs composantes de tendance, saisonnalité et aléa représentatif du risque. D'autre part les performances de la distribution, évaluées à partir d'une analyse des différentiels de prix entre stades de gros et de détail. Les quinze principaux légumes ont ainsi été classés selon l'importance de la variabilité de leur prix et la contribution de chaque composante. Il ressort de cette décomposition des prix que les aléas constituent le principal facteur de variabilité. Les produits connaissant les aléas les plus forts sont la petite tomate, le chou-fleur, le piment et le poivron. La saisonnalité n'apporte une contribution majeure à la variabilité des prix que dans les cas de la pomme de terre et du haricot demi-sec. La composante de tendance est nulle sur la période 1993-1998 pour la majorité des produits. Les différentiels de prix entre stades de gros à St Pierre et de détail à St Denis sont contrastés selon le circuit, marché forain ou grande distribution. Le marché forain présente une meilleure compétitivité en terme de prix et accroît encore son avantage durant la période 1994-1998. La tendance des différentiels est en effet à la baisse pour les marchés forains et stationnaire pour la grande distribution. L'évolution de la structure des prix dans la filière légumes n'est donc pas défavorable aux producteurs, contrairement au cas d'autres filières agricoles. (Résumé d'auteur
Directed Subset Feedback Vertex Set Is Fixed-Parameter Tractable
Given a graph and an integer , the Feedback Vertex Set (FVS) problem
asks if there is a vertex set of size at most that hits all cycles in
the graph. The fixed-parameter tractability status of FVS in directed graphs
was a long-standing open problem until Chen et al. (STOC '08) showed that it is
FPT by giving a time algorithm. In the subset versions of
this problems, we are given an additional subset of vertices (resp., edges)
and we want to hit all cycles passing through a vertex of (resp. an edge of
). Recently, the Subset Feedback Vertex Set in undirected graphs was shown
to be FPT by Cygan et al. (ICALP '11) and independently by Kakimura et al.
(SODA '12). We generalize the result of Chen et al. (STOC '08) by showing that
Subset Feedback Vertex Set in directed graphs can be solved in time
. By our result, we complete the picture for feedback
vertex set problems and their subset versions in undirected and directed
graphs. Besides proving the fixed-parameter tractability of Directed Subset
Feedback Vertex Set, we reformulate the random sampling of important separators
technique in an abstract way that can be used for a general family of
transversal problems. Moreover, we modify the probability distribution used in
the technique to achieve better running time; in particular, this gives an
improvement from to in the parameter dependence of
the Directed Multiway Cut algorithm of Chitnis et al. (SODA '12).Comment: To appear in ACM Transactions on Algorithms. A preliminary version
appeared in ICALP '12. We would like to thank Marcin Pilipczuk for pointing
out a missing case in the conference version which has been considered in
this version. Also, we give an single exponential FPT algorithm improving on
the double exponential algorithm from the conference versio
Polynomial Kernelization for Removing Induced Claws and Diamonds
A graph is called (claw,diamond)-free if it contains neither a claw (a ) nor a diamond (a with an edge removed) as an induced subgraph. Equivalently, (claw,diamond)-free graphs can be characterized as line graphs of triangle-free graphs, or as linear dominoes, i.e., graphs in which every vertex is in at most two maximal cliques and every edge is in exactly one maximal clique. In this paper we consider the parameterized complexity of the (claw,diamond)-free Edge Deletion problem, where given a graph and a parameter , the question is whether one can remove at most edges from to obtain a (claw,diamond)-free graph. Our main result is that this problem admits a polynomial kernel. We complement this finding by proving that, even on instances with maximum degree , the problem is NP-complete and cannot be solved in time unless the Exponential Time Hypothesis fai
Fast algorithms for min independent dominating set
We first devise a branching algorithm that computes a minimum independent
dominating set on any graph with running time O*(2^0.424n) and polynomial
space. This improves the O*(2^0.441n) result by (S. Gaspers and M. Liedloff, A
branch-and-reduce algorithm for finding a minimum independent dominating set in
graphs, Proc. WG'06). We then show that, for every r>3, it is possible to
compute an r-((r-1)/r)log_2(r)-approximate solution for min independent
dominating set within time O*(2^(nlog_2(r)/r))
Assigning channels via the meet-in-the-middle approach
We study the complexity of the Channel Assignment problem. By applying the
meet-in-the-middle approach we get an algorithm for the -bounded Channel
Assignment (when the edge weights are bounded by ) running in time
. This is the first algorithm which breaks the
barrier. We extend this algorithm to the counting variant, at the
cost of slightly higher polynomial factor.
A major open problem asks whether Channel Assignment admits a -time
algorithm, for a constant independent of . We consider a similar
question for Generalized T-Coloring, a CSP problem that generalizes \CA. We
show that Generalized T-Coloring does not admit a
-time algorithm, where is the
size of the instance.Comment: SWAT 2014: 282-29
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