2,735 research outputs found
A New Push-Relabel Algorithm for Sparse Networks
In this paper, we present a new push-relabel algorithm for the maximum flow
problem on flow networks with vertices and arcs. Our algorithm computes
a maximum flow in time on sparse networks where . To our
knowledge, this is the first time push-relabel algorithm for the edge case; previously, it was known that push-relabel implementations
could find a max-flow in time when (King,
et. al., SODA `92). This also matches a recent flow decomposition-based
algorithm due to Orlin (STOC `13), which finds a max-flow in time on
sparse networks.
Our main result is improving on the Excess-Scaling algorithm (Ahuja & Orlin,
1989) by reducing the number of nonsaturating pushes to across all
scaling phases. This is reached by combining Ahuja and Orlin's algorithm with
Orlin's compact flow networks. A contribution of this paper is demonstrating
that the compact networks technique can be extended to the push-relabel family
of algorithms. We also provide evidence that this approach could be a promising
avenue towards an -time algorithm for all edge densities.Comment: 23 pages. arXiv admin note: substantial text overlap with
arXiv:1309.2525 - This version includes an extension of the result to the
O(n) edge cas
Improved Compact Visibility Representation of Planar Graph via Schnyder's Realizer
Let be an -node planar graph. In a visibility representation of ,
each node of is represented by a horizontal line segment such that the line
segments representing any two adjacent nodes of are vertically visible to
each other. In the present paper we give the best known compact visibility
representation of . Given a canonical ordering of the triangulated , our
algorithm draws the graph incrementally in a greedy manner. We show that one of
three canonical orderings obtained from Schnyder's realizer for the
triangulated yields a visibility representation of no wider than
. Our easy-to-implement O(n)-time algorithm bypasses the
complicated subroutines for four-connected components and four-block trees
required by the best previously known algorithm of Kant. Our result provides a
negative answer to Kant's open question about whether is a
worst-case lower bound on the required width. Also, if has no degree-three
(respectively, degree-five) internal node, then our visibility representation
for is no wider than (respectively, ).
Moreover, if is four-connected, then our visibility representation for
is no wider than , matching the best known result of Kant and He. As a
by-product, we obtain a much simpler proof for a corollary of Wagner's Theorem
on realizers, due to Bonichon, Sa\"{e}c, and Mosbah.Comment: 11 pages, 6 figures, the preliminary version of this paper is to
appear in Proceedings of the 20th Annual Symposium on Theoretical Aspects of
Computer Science (STACS), Berlin, Germany, 200
Chain Reduction for Binary and Zero-Suppressed Decision Diagrams
Chain reduction enables reduced ordered binary decision diagrams (BDDs) and
zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the
others' ability to symbolically represent Boolean functions in compact form.
For any Boolean function, its chain-reduced ZDD (CZDD) representation will be
no larger than its ZDD representation, and at most twice the size of its BDD
representation. The chain-reduced BDD (CBDD) of a function will be no larger
than its BDD representation, and at most three times the size of its CZDD
representation. Extensions to the standard algorithms for operating on BDDs and
ZDDs enable them to operate on the chain-reduced versions. Experimental
evaluations on representative benchmarks for encoding word lists, solving
combinatorial problems, and operating on digital circuits indicate that chain
reduction can provide significant benefits in terms of both memory and
execution time
Universality and diversity of folding mechanics for three-helix bundle proteins
In this study we evaluate, at full atomic detail, the folding processes of
two small helical proteins, the B domain of protein A and the Villin headpiece.
Folding kinetics are studied by performing a large number of ab initio Monte
Carlo folding simulations using a single transferable all-atom potential. Using
these trajectories, we examine the relaxation behavior, secondary structure
formation, and transition-state ensembles (TSEs) of the two proteins and
compare our results with experimental data and previous computational studies.
To obtain a detailed structural information on the folding dynamics viewed as
an ensemble process, we perform a clustering analysis procedure based on graph
theory. Moreover, rigorous pfold analysis is used to obtain representative
samples of the TSEs and a good quantitative agreement between experimental and
simulated Fi-values is obtained for protein A. Fi-values for Villin are also
obtained and left as predictions to be tested by future experiments. Our
analysis shows that two-helix hairpin is a common partially stable structural
motif that gets formed prior to entering the TSE in the studied proteins. These
results together with our earlier study of Engrailed Homeodomain and recent
experimental studies provide a comprehensive, atomic-level picture of folding
mechanics of three-helix bundle proteins.Comment: PNAS, in press, revised versio
Identifying gene locus associations with promyelocytic leukemia nuclear bodies using immuno-TRAP.
Important insights into nuclear function would arise if gene loci physically interacting with particular subnuclear domains could be readily identified. Immunofluorescence microscopy combined with fluorescence in situ hybridization (immuno-FISH), the method that would typically be used in such a study, is limited by spatial resolution and requires prior assumptions for selecting genes to probe. Our new technique, immuno-TRAP, overcomes these limitations. Using promyelocytic leukemia nuclear bodies (PML NBs) as a model, we used immuno-TRAP to determine if specific genes localize within molecular dimensions with these bodies. Although we confirmed a TP53 gene-PML NB association, immuno-TRAP allowed us to uncover novel locus-PML NB associations, including the ABCA7 and TFF1 loci and, most surprisingly, the PML locus itself. These associations were cell type specific and reflected the cell's physiological state. Combined with microarrays or deep sequencing, immuno-TRAP provides powerful opportunities for identifying gene locus associations with potentially any nuclear subcompartment
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