7,596 research outputs found
Typical Sequences Revisited — Computing Width Parameters of Graphs
In this work, we give a structural lemma on merges of typical sequences, a notion that was introduced in 1991 [Lagergren and Arnborg, Bodlaender and Kloks, both ICALP 1991] to obtain constructive linear time parameterized algorithms for treewidth and pathwidth. The lemma addresses a runtime bottleneck in those algorithms but so far it does not lead to asymptotically faster algorithms. However, we apply the lemma to show that the cutwidth and the modified cutwidth of series parallel digraphs can be computed in polynomial time
Clearing Contamination in Large Networks
In this work, we study the problem of clearing contamination spreading
through a large network where we model the problem as a graph searching game.
The problem can be summarized as constructing a search strategy that will leave
the graph clear of any contamination at the end of the searching process in as
few steps as possible. We show that this problem is NP-hard even on directed
acyclic graphs and provide an efficient approximation algorithm. We
experimentally observe the performance of our approximation algorithm in
relation to the lower bound on several large online networks including
Slashdot, Epinions and Twitter. The experiments reveal that in most cases our
algorithm performs near optimally
A Unifying Framework for Characterizing and Computing Width Measures
Algorithms for computing or approximating optimal decompositions for decompositional parameters such as treewidth or clique-width have so far traditionally been tailored to specific width parameters. Moreover, for mim-width, no efficient algorithms for computing good decompositions were known, even under highly restrictive parameterizations. In this work we identify ?-branchwidth as a class of generic decompositional parameters that can capture mim-width, treewidth, clique-width as well as other measures. We show that while there is an infinite number of ?-branchwidth parameters, only a handful of these are asymptotically distinct. We then develop fixed-parameter and kernelization algorithms (under several structural parameterizations) that can approximate every possible ?-branchwidth, providing a unifying parameterized framework that can efficiently obtain near-optimal tree-decompositions, k-expressions, as well as optimal mim-width decompositions
A Linear Fixed Parameter Tractable Algorithm for Connected Pathwidth
International audienceThe graph parameter of {\sl pathwidth} can be seen as a measure of the topological resemblance of a graph to a path. A popular definition of pathwidth is given in terms of {\sl node search} where we are given a system of tunnels (represented by a graph) that is contaminated by some infectious substance and we are looking for a search strategy that, at each step, either places a searcher on a vertex or removes a searcher from a vertex and where an edge is cleaned when both endpoints are simultaneously occupied by searchers. It was proved that the minimum number of searchers required for a successful cleaning strategy is equal to the pathwidth of the graph plus one.Two desired characteristics for a cleaning strategy is to be {\sl monotone} (no recontamination occurs) and {\sl connected} (clean territories always remain connected). Under these two demands, the number of searchers is equivalent to a variant of pathwidth called {\em connected pathwidth}. We prove that connected pathwidth is fixed parameter tractable, in particular we design a time algorithm that checks whether the connected pathwidth of is at most This resolves an open question by [{\sl Dereniowski, Osula, and Rz{\k{a}}{\.{z}}ewski, Finding small-width connected path-decompositions in polynomial time. Theor. Comput. Sci., 794:85–100, 2019}\,]. For our algorithm, we enrich the {\sl typical sequence technique} that is able to deal with the connectivity demand. Typical sequences have been introduced in [{\sl Bodlaender and Kloks. Efficient and constructive algorithms for the pathwidth and treewidth of graphs. J. Algorithms, 21(2):358–402, 1996}\,] for the design of linear parameterized algorithms for treewidth and pathwidth. While this technique has been later applied to other parameters, none of its advancements was able to deal with the connectivity demand, as it is a ``global’’ demand that concerns an unbounded number of parts of the graph of unbounded size. The proposed extension is based on an encoding of the connectivity property that is quite versatile and may be adapted so to deliver linear parameterized algorithms for the connected variants of other width parameters as well. An immediate consequence of our result is a time algorithm for the monotone and connected version of the edge search number
Connection Matrices and the Definability of Graph Parameters
In this paper we extend and prove in detail the Finite Rank Theorem for
connection matrices of graph parameters definable in Monadic Second Order Logic
with counting (CMSOL) from B. Godlin, T. Kotek and J.A. Makowsky (2008) and
J.A. Makowsky (2009). We demonstrate its vast applicability in simplifying
known and new non-definability results of graph properties and finding new
non-definability results for graph parameters. We also prove a Feferman-Vaught
Theorem for the logic CFOL, First Order Logic with the modular counting
quantifiers
A Causal And-Or Graph Model for Visibility Fluent Reasoning in Tracking Interacting Objects
Tracking humans that are interacting with the other subjects or environment
remains unsolved in visual tracking, because the visibility of the human of
interests in videos is unknown and might vary over time. In particular, it is
still difficult for state-of-the-art human trackers to recover complete human
trajectories in crowded scenes with frequent human interactions. In this work,
we consider the visibility status of a subject as a fluent variable, whose
change is mostly attributed to the subject's interaction with the surrounding,
e.g., crossing behind another object, entering a building, or getting into a
vehicle, etc. We introduce a Causal And-Or Graph (C-AOG) to represent the
causal-effect relations between an object's visibility fluent and its
activities, and develop a probabilistic graph model to jointly reason the
visibility fluent change (e.g., from visible to invisible) and track humans in
videos. We formulate this joint task as an iterative search of a feasible
causal graph structure that enables fast search algorithm, e.g., dynamic
programming method. We apply the proposed method on challenging video sequences
to evaluate its capabilities of estimating visibility fluent changes of
subjects and tracking subjects of interests over time. Results with comparisons
demonstrate that our method outperforms the alternative trackers and can
recover complete trajectories of humans in complicated scenarios with frequent
human interactions.Comment: accepted by CVPR 201
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