207 research outputs found
Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic
The hypergraph duality problem DUAL is defined as follows: given two simple
hypergraphs and , decide whether
consists precisely of all minimal transversals of (in which case
we say that is the dual of ). This problem is
equivalent to deciding whether two given non-redundant monotone DNFs are dual.
It is known that non-DUAL, the complementary problem to DUAL, is in
, where
denotes the complexity class of all problems that after a nondeterministic
guess of bits can be decided (checked) within complexity class
. It was conjectured that non-DUAL is in . In this paper we prove this conjecture and actually
place the non-DUAL problem into the complexity class which is a subclass of . We here refer to the logtime-uniform version of
, which corresponds to , i.e., first order
logic augmented by counting quantifiers. We achieve the latter bound in two
steps. First, based on existing problem decomposition methods, we develop a new
nondeterministic algorithm for non-DUAL that requires to guess
bits. We then proceed by a logical analysis of this algorithm, allowing us to
formulate its deterministic part in . From this result, by
the well known inclusion , it follows
that DUAL belongs also to . Finally, by exploiting
the principles on which the proposed nondeterministic algorithm is based, we
devise a deterministic algorithm that, given two hypergraphs and
, computes in quadratic logspace a transversal of
missing in .Comment: Restructured the presentation in order to be the extended version of
a paper that will shortly appear in SIAM Journal on Computin
Application of hypergraphs in decomposition of discrete systems
seria: Lecture Notes in Control and Computer Science ; vol. 23
An Efficient Architecture for Information Retrieval in P2P Context Using Hypergraph
Peer-to-peer (P2P) Data-sharing systems now generate a significant portion of
Internet traffic. P2P systems have emerged as an accepted way to share enormous
volumes of data. Needs for widely distributed information systems supporting
virtual organizations have given rise to a new category of P2P systems called
schema-based. In such systems each peer is a database management system in
itself, ex-posing its own schema. In such a setting, the main objective is the
efficient search across peer databases by processing each incoming query
without overly consuming bandwidth. The usability of these systems depends on
successful techniques to find and retrieve data; however, efficient and
effective routing of content-based queries is an emerging problem in P2P
networks. This work was attended as an attempt to motivate the use of mining
algorithms in the P2P context may improve the significantly the efficiency of
such methods. Our proposed method based respectively on combination of
clustering with hypergraphs. We use ECCLAT to build approximate clustering and
discovering meaningful clusters with slight overlapping. We use an algorithm
MTMINER to extract all minimal transversals of a hypergraph (clusters) for
query routing. The set of clusters improves the robustness in queries routing
mechanism and scalability in P2P Network. We compare the performance of our
method with the baseline one considering the queries routing problem. Our
experimental results prove that our proposed methods generate impressive levels
of performance and scalability with with respect to important criteria such as
response time, precision and recall.Comment: 2o pages, 8 figure
Efficiently Enumerating Hitting Sets of Hypergraphs Arising in Data Profiling
We devise an enumeration method for inclusion-wise minimal hitting sets in hypergraphs. It has delay O(mk* +1 · n2) and uses linear space. Hereby, n is the number of vertices, m the number of hyperedges, and k* the rank of the transversal hypergraph. In particular, on classes of hypergraphs for which the cardinality k* of the largest minimal hitting set is bounded, the delay is polynomial. The algorithm solves the extension problem for minimal hitting sets as a subroutine. We show that the extension problem is W[3]-complete when parameterised by the cardinality of the set which is to be extended. For the subroutine, we give an algorithm that is optimal under the exponential time hypothesis. Despite these lower bounds, we provide empirical evidence showing that the enumeration outperforms the theoretical worst-case guarantee on hypergraphs arising in the profiling of relational databases, namely, in the detection of unique column combinations
GPU accelerated maximum cardinality matching algorithms for bipartite graphs
We design, implement, and evaluate GPU-based algorithms for the maximum
cardinality matching problem in bipartite graphs. Such algorithms have a
variety of applications in computer science, scientific computing,
bioinformatics, and other areas. To the best of our knowledge, ours is the
first study which focuses on GPU implementation of the maximum cardinality
matching algorithms. We compare the proposed algorithms with serial and
multicore implementations from the literature on a large set of real-life
problems where in majority of the cases one of our GPU-accelerated algorithms
is demonstrated to be faster than both the sequential and multicore
implementations.Comment: 14 pages, 5 figure
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