5,381 research outputs found
Parameterized complexity of the MINCCA problem on graphs of bounded decomposability
In an edge-colored graph, the cost incurred at a vertex on a path when two
incident edges with different colors are traversed is called reload or
changeover cost. The "Minimum Changeover Cost Arborescence" (MINCCA) problem
consists in finding an arborescence with a given root vertex such that the
total changeover cost of the internal vertices is minimized. It has been
recently proved by G\"oz\"upek et al. [TCS 2016] that the problem is FPT when
parameterized by the treewidth and the maximum degree of the input graph. In
this article we present the following results for the MINCCA problem:
- the problem is W[1]-hard parameterized by the treedepth of the input graph,
even on graphs of average degree at most 8. In particular, it is W[1]-hard
parameterized by the treewidth of the input graph, which answers the main open
problem of G\"oz\"upek et al. [TCS 2016];
- it is W[1]-hard on multigraphs parameterized by the tree-cutwidth of the
input multigraph;
- it is FPT parameterized by the star tree-cutwidth of the input graph, which
is a slightly restricted version of tree-cutwidth. This result strictly
generalizes the FPT result given in G\"oz\"upek et al. [TCS 2016];
- it remains NP-hard on planar graphs even when restricted to instances with
at most 6 colors and 0/1 symmetric costs, or when restricted to instances with
at most 8 colors, maximum degree bounded by 4, and 0/1 symmetric costs.Comment: 25 pages, 11 figure
Pair-Linking for Collective Entity Disambiguation: Two Could Be Better Than All
Collective entity disambiguation aims to jointly resolve multiple mentions by
linking them to their associated entities in a knowledge base. Previous works
are primarily based on the underlying assumption that entities within the same
document are highly related. However, the extend to which these mentioned
entities are actually connected in reality is rarely studied and therefore
raises interesting research questions. For the first time, we show that the
semantic relationships between the mentioned entities are in fact less dense
than expected. This could be attributed to several reasons such as noise, data
sparsity and knowledge base incompleteness. As a remedy, we introduce MINTREE,
a new tree-based objective for the entity disambiguation problem. The key
intuition behind MINTREE is the concept of coherence relaxation which utilizes
the weight of a minimum spanning tree to measure the coherence between
entities. Based on this new objective, we design a novel entity disambiguation
algorithms which we call Pair-Linking. Instead of considering all the given
mentions, Pair-Linking iteratively selects a pair with the highest confidence
at each step for decision making. Via extensive experiments, we show that our
approach is not only more accurate but also surprisingly faster than many
state-of-the-art collective linking algorithms
Invasion percolation on the Poisson-weighted infinite tree
We study invasion percolation on Aldous' Poisson-weighted infinite tree, and
derive two distinct Markovian representations of the resulting process. One of
these is the limit of a representation discovered by Angel et
al. [Ann. Appl. Probab. 36 (2008) 420-466]. We also introduce an exploration
process of a randomly weighted Poisson incipient infinite cluster. The dynamics
of the new process are much more straightforward to describe than those of
invasion percolation, but it turns out that the two processes have extremely
similar behavior. Finally, we introduce two new "stationary" representations of
the Poisson incipient infinite cluster as random graphs on which
are, in particular, factors of a homogeneous Poisson point process on the upper
half-plane .Comment: Published in at http://dx.doi.org/10.1214/11-AAP761 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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