73 research outputs found
Wikipedia Page Classification
Cílem této práce je navrhnout a implementovat systém, který umožní výběr tematicky zaměřených článků z Wikipedie za účelem úspory místa při jejím offline uložení. Řešení tohoto problému je dosaženo s využitím metod spadajících do oblasti vyhledávání informací a jejich konkrétní implementací v rámci nástroje Elasticsearch. Systém se na základě zadaných klíčových slov snaží určit, o jakou tematickou oblast se uživatel zajímá a články z této oblasti zařadit do výsledného výběru. K tomu využívá především mechanismy pro určení podobných dokumentů a zahrnutí všech článků z kategorií, které se ve výběru často opakují. Velikosti souborů generovaných výsledným systémem na základě dotazů nad Simple English Wikipedia se obvykle pohybují pod 30 MB.The goal of this paper is to design and implement a system for selection of Wikipedia articles relevant to a given topic in order to reduce the amount of memory taken by its offline version. The solution of this problem was achieved with use of methods from information retrieval and theirs implementation using Elasticsearch search engine. The system tries to determine the area of user's interest by given keywords and make a selection of articles from that area. This is achieved by measuring of similarity of articles and adding all articles from frequent categories in the selection. The sizes of the output files for queries over Simple English Wikipedia are usually below 30 MB.
Minimum Eccentricity Shortest Path Problem with Respect to Structural Parameters
The Minimum Eccentricity Shortest Path Problem consists in finding a shortest
path with minimum eccentricity in a given undirected graph. The problem is
known to be NP-complete and W[2]-hard with respect to the desired eccentricity.
We present fpt algorithms for the problem parameterized by the modular width,
distance to cluster graph, the combination of distance to disjoint paths with
the desired eccentricity, and maximum leaf number
Generating faster algorithms for d-Path Vertex Cover
Many algorithms which exactly solve hard problems require branching on more
or less complex structures in order to do their job. Those who design such
algorithms often find themselves doing a meticulous analysis of numerous
different cases in order to identify these structures and design suitable
branching rules, all done by hand. This process tends to be error prone and
often the resulting algorithm may be difficult to implement in practice.
In this work, we aim to automate a part of this process and focus on
simplicity of the resulting implementation.
We showcase our approach on the following problem. For a constant , the
-Path Vertex Cover problem (-PVC) is as follows: Given an undirected
graph and an integer , find a subset of at most vertices of the graph,
such that their deletion results in a graph not containing a path on
vertices as a subgraph. We develop a fully automated framework to generate
parameterized branching algorithms for the problem and obtain algorithms
outperforming those previously known for . E.g., we show that
-PVC can be solved in time
Complexity of the Steiner Network Problem with Respect to the Number of Terminals
In the Directed Steiner Network problem we are given an arc-weighted digraph
, a set of terminals , and an (unweighted) directed
request graph with . Our task is to output a subgraph of the minimum cost such that there is a directed path from to in
for all .
It is known that the problem can be solved in time
[Feldman&Ruhl, SIAM J. Comput. 2006] and cannot be solved in time
even if is planar, unless Exponential-Time Hypothesis
(ETH) fails [Chitnis et al., SODA 2014]. However, as this reduction (and other
reductions showing hardness of the problem) only shows that the problem cannot
be solved in time unless ETH fails, there is a significant
gap in the complexity with respect to in the exponent.
We show that Directed Steiner Network is solvable in time , where is a constant depending solely on the
genus of and is a computable function. We complement this result by
showing that there is no algorithm for
any function for the problem on general graphs, unless ETH fails
Beyond Max-Cut: \lambda-Extendible Properties Parameterized Above the Poljak-Turz\'{i}k Bound
Poljak and Turz\'ik (Discrete Math. 1986) introduced the notion of
\lambda-extendible properties of graphs as a generalization of the property of
being bipartite. They showed that for any 0<\lambda<1 and \lambda-extendible
property \Pi, any connected graph G on n vertices and m edges contains a
subgraph H \in {\Pi} with at least \lambda m+ (1-\lambda)/2 (n-1) edges. The
property of being bipartite is 1/2-extendible, and thus this bound generalizes
the Edwards-Erd\H{o}s bound for Max-Cut.
We define a variant, namely strong \lambda-extendibility, to which the bound
applies. For a strongly \lambda-extendible graph property \Pi, we define the
parameterized Above Poljak- Turz\'ik (APT) (\Pi) problem as follows: Given a
connected graph G on n vertices and m edges and an integer parameter k, does
there exist a spanning subgraph H of G such that H \in {\Pi} and H has at least
\lambda m + (1-\lambda)/2 (n - 1) + k edges? The parameter is k, the surplus
over the number of edges guaranteed by the Poljak-Turz\'ik bound.
We consider properties {\Pi} for which APT (\Pi) is fixed- parameter
tractable (FPT) on graphs which are O(k) vertices away from being a graph in
which each block is a clique. We show that for all such properties, APT (\Pi)
is FPT for all 0<\lambda<1. Our results hold for properties of oriented graphs
and graphs with edge labels. Our results generalize the result of Crowston et
al. (ICALP 2012) on Max-Cut parameterized above the Edwards-Erd\H{o}s bound,
and yield FPT algorithms for several graph problems parameterized above lower
bounds, e.g., Max q-Colorable Subgraph problem. Our results also imply that the
parameterized above-guarantee Oriented Max Acyclic Digraph problem is FPT, thus
solving an open question of Raman and Saurabh (Theor. Comput. Sci. 2006).Comment: 23 pages, no figur
A Parameterized Complexity View on Collapsing k-Cores
We study the NP-hard graph problem COLLAPSED K-CORE where, given an undirected graph G and integers b, x, and k, we are asked to remove b vertices such that the k-core of remaining graph, that is, the (uniquely determined) largest induced subgraph with minimum degree k, has size at most x. COLLAPSED K-CORE was introduced by Zhang et al. (2017) and it is motivated by the study of engagement behavior of users in a social network and measuring the resilience of a network against user drop outs. COLLAPSED K-CORE is a generalization of R-DEGENERATE VERTEX DELETION (which is known to be NP-hard for all r ≥ 0) where, given an undirected graph G and integers b and r, we are asked to remove b vertices such that the remaining graph is r-degenerate, that is, every its subgraph has minimum degree at most r. We investigate the parameterized complexity of COLLAPSED K-CORE with respect to the parameters b, x, and k, and several structural parameters of the input graph. We reveal a dichotomy in the computational complexity of COLLAPSED K-CORE for k ≤ 2 and k ≥ 3. For the latter case it is known that for all x ≥ 0 COLLAPSED K-CORE is W[P]-hard when parameterized by b. For k ≤ 2 we show that COLLAPSED K-CORE is W[1]-hard when parameterized by b and in FPT when parameterized by (b + x). Furthermore, we outline that COLLAPSED K-CORE is in FPT when parameterized by the treewidth of the input graph and presumably does not admit a polynomial kernel when parameterized by the vertex cover number of the input graph.DFG, 284041127, Algorithmen für Faire Allokationen (AFFA)DFG, 382063982, Multivariate Algorithmik temporaler Graphprobleme (MATE)TU Berlin, Open-Access-Mittel – 202
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