252,023 research outputs found
Parameterized Complexity Results for General Factors in Bipartite Graphs with an Application to Constraint Programming
The NP-hard general factor problem asks, given a graph and for each vertex a
list of integers, whether the graph has a spanning subgraph where each vertex
has a degree that belongs to its assigned list. The problem remains NP-hard
even if the given graph is bipartite with partition U+V, and each vertex in U
is assigned the list {1}; this subproblem appears in the context of constraint
programming as the consistency problem for the extended global cardinality
constraint. We show that this subproblem is fixed-parameter tractable when
parameterized by the size of the second partite set V. More generally, we show
that the general factor problem for bipartite graphs, parameterized by |V|, is
fixed-parameter tractable as long as all vertices in U are assigned lists of
length 1, but becomes W[1]-hard if vertices in U are assigned lists of length
at most 2. We establish fixed-parameter tractability by reducing the problem
instance to a bounded number of acyclic instances, each of which can be solved
in polynomial time by dynamic programming.Comment: Full version of a paper that appeared in preliminary form in the
proceedings of IPEC'1
Ranking Medical Subject Headings using a factor graph model.
Automatically assigning MeSH (Medical Subject Headings) to articles is an active research topic. Recent work demonstrated the feasibility of improving the existing automated Medical Text Indexer (MTI) system, developed at the National Library of Medicine (NLM). Encouraged by this work, we propose a novel data-driven approach that uses semantic distances in the MeSH ontology for automated MeSH assignment. Specifically, we developed a graphical model to propagate belief through a citation network to provide robust MeSH main heading (MH) recommendation. Our preliminary results indicate that this approach can reach high Mean Average Precision (MAP) in some scenarios
Local algorithms in (weakly) coloured graphs
A local algorithm is a distributed algorithm that completes after a constant
number of synchronous communication rounds. We present local approximation
algorithms for the minimum dominating set problem and the maximum matching
problem in 2-coloured and weakly 2-coloured graphs. In a weakly 2-coloured
graph, both problems admit a local algorithm with the approximation factor
, where is the maximum degree of the graph. We also give
a matching lower bound proving that there is no local algorithm with a better
approximation factor for either of these problems. Furthermore, we show that
the stronger assumption of a 2-colouring does not help in the case of the
dominating set problem, but there is a local approximation scheme for the
maximum matching problem in 2-coloured graphs.Comment: 14 pages, 3 figure
A survey on algorithmic aspects of modular decomposition
The modular decomposition is a technique that applies but is not restricted
to graphs. The notion of module naturally appears in the proofs of many graph
theoretical theorems. Computing the modular decomposition tree is an important
preprocessing step to solve a large number of combinatorial optimization
problems. Since the first polynomial time algorithm in the early 70's, the
algorithmic of the modular decomposition has known an important development.
This paper survey the ideas and techniques that arose from this line of
research
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