7,143 research outputs found
Cycle and Circle Tests of Balance in Gain Graphs: Forbidden Minors and Their Groups
We examine two criteria for balance of a gain graph, one based on binary
cycles and one on circles. The graphs for which each criterion is valid depend
on the set of allowed gain groups. The binary cycle test is invalid, except for
forests, if any possible gain group has an element of odd order. Assuming all
groups are allowed, or all abelian groups, or merely the cyclic group of order
3, we characterize, both constructively and by forbidden minors, the graphs for
which the circle test is valid. It turns out that these three classes of groups
have the same set of forbidden minors. The exact reason for the importance of
the ternary cyclic group is not clear.Comment: 19 pages, 3 figures. Format: Latex2e. Changes: minor. To appear in
Journal of Graph Theor
Powers of Hamilton cycles in pseudorandom graphs
We study the appearance of powers of Hamilton cycles in pseudorandom graphs,
using the following comparatively weak pseudorandomness notion. A graph is
-pseudorandom if for all disjoint and with and we have
. We prove that for all there is an
such that an -pseudorandom graph on
vertices with minimum degree at least contains the square of a
Hamilton cycle. In particular, this implies that -graphs with
contain the square of a Hamilton cycle, and thus
a triangle factor if is a multiple of . This improves on a result of
Krivelevich, Sudakov and Szab\'o [Triangle factors in sparse pseudo-random
graphs, Combinatorica 24 (2004), no. 3, 403--426].
We also extend our result to higher powers of Hamilton cycles and establish
corresponding counting versions.Comment: 30 pages, 1 figur
THE ELECTRONIC JOURNAL OF COMBINATORICS (2014), DS1.14 References
and Computing 11. The results of 143 references depend on computer algorithms. The references are ordered alphabetically by the last name of the first author, and where multiple papers have the same first author they are ordered by the last name of the second author, etc. We preferred that all work by the same author be in consecutive positions. Unfortunately, this causes that some of the abbreviations are not in alphabetical order. For example, [BaRT] is earlier on the list than [BaLS]. We also wish to explain a possible confusion with respect to the order of parts and spelling of Chinese names. We put them without any abbreviations, often with the last name written first as is customary in original. Sometimes this is different from the citations in other sources. One can obtain all variations of writing any specific name by consulting the authors database of Mathematical Reviews a
Planar graph coloring avoiding monochromatic subgraphs: trees and paths make things difficult
We consider the problem of coloring a planar graph with the minimum number of colors such that each color class avoids one or more forbidden graphs as subgraphs. We perform a detailed study of the computational complexity of this problem
Characterizations of Pseudo-Codewords of LDPC Codes
An important property of high-performance, low complexity codes is the
existence of highly efficient algorithms for their decoding. Many of the most
efficient, recent graph-based algorithms, e.g. message passing algorithms and
decoding based on linear programming, crucially depend on the efficient
representation of a code in a graphical model. In order to understand the
performance of these algorithms, we argue for the characterization of codes in
terms of a so called fundamental cone in Euclidean space which is a function of
a given parity check matrix of a code, rather than of the code itself. We give
a number of properties of this fundamental cone derived from its connection to
unramified covers of the graphical models on which the decoding algorithms
operate. For the class of cycle codes, these developments naturally lead to a
characterization of the fundamental polytope as the Newton polytope of the
Hashimoto edge zeta function of the underlying graph.Comment: Submitted, August 200
Generalized Points-to Graphs: A New Abstraction of Memory in the Presence of Pointers
Flow- and context-sensitive points-to analysis is difficult to scale; for
top-down approaches, the problem centers on repeated analysis of the same
procedure; for bottom-up approaches, the abstractions used to represent
procedure summaries have not scaled while preserving precision.
We propose a novel abstraction called the Generalized Points-to Graph (GPG)
which views points-to relations as memory updates and generalizes them using
the counts of indirection levels leaving the unknown pointees implicit. This
allows us to construct GPGs as compact representations of bottom-up procedure
summaries in terms of memory updates and control flow between them. Their
compactness is ensured by the following optimizations: strength reduction
reduces the indirection levels, redundancy elimination removes redundant memory
updates and minimizes control flow (without over-approximating data dependence
between memory updates), and call inlining enhances the opportunities of these
optimizations. We devise novel operations and data flow analyses for these
optimizations.
Our quest for scalability of points-to analysis leads to the following
insight: The real killer of scalability in program analysis is not the amount
of data but the amount of control flow that it may be subjected to in search of
precision. The effectiveness of GPGs lies in the fact that they discard as much
control flow as possible without losing precision (i.e., by preserving data
dependence without over-approximation). This is the reason why the GPGs are
very small even for main procedures that contain the effect of the entire
program. This allows our implementation to scale to 158kLoC for C programs
Social Network Analysis with sna
Modern social network analysis---the analysis of relational data arising from social systems---is a computationally intensive area of research. Here, we provide an overview of a software package which provides support for a range of network analytic functionality within the R statistical computing environment. General categories of currently supported functionality are described, and brief examples of package syntax and usage are shown.
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