1,985 research outputs found
Fast Computation of Small Cuts via Cycle Space Sampling
We describe a new sampling-based method to determine cuts in an undirected
graph. For a graph (V, E), its cycle space is the family of all subsets of E
that have even degree at each vertex. We prove that with high probability,
sampling the cycle space identifies the cuts of a graph. This leads to simple
new linear-time sequential algorithms for finding all cut edges and cut pairs
(a set of 2 edges that form a cut) of a graph.
In the model of distributed computing in a graph G=(V, E) with O(log V)-bit
messages, our approach yields faster algorithms for several problems. The
diameter of G is denoted by Diam, and the maximum degree by Delta. We obtain
simple O(Diam)-time distributed algorithms to find all cut edges,
2-edge-connected components, and cut pairs, matching or improving upon previous
time bounds. Under natural conditions these new algorithms are universally
optimal --- i.e. a Omega(Diam)-time lower bound holds on every graph. We obtain
a O(Diam+Delta/log V)-time distributed algorithm for finding cut vertices; this
is faster than the best previous algorithm when Delta, Diam = O(sqrt(V)). A
simple extension of our work yields the first distributed algorithm with
sub-linear time for 3-edge-connected components. The basic distributed
algorithms are Monte Carlo, but they can be made Las Vegas without increasing
the asymptotic complexity.
In the model of parallel computing on the EREW PRAM our approach yields a
simple algorithm with optimal time complexity O(log V) for finding cut pairs
and 3-edge-connected components.Comment: Previous version appeared in Proc. 35th ICALP, pages 145--160, 200
Cycle decompositions: from graphs to continua
We generalise a fundamental graph-theoretical fact, stating that every
element of the cycle space of a graph is a sum of edge-disjoint cycles, to
arbitrary continua. To achieve this we replace graph cycles by topological
circles, and replace the cycle space of a graph by a new homology group for
continua which is a quotient of the first singular homology group . This
homology seems to be particularly apt for studying spaces with infinitely
generated , e.g. infinite graphs or fractals.Comment: Advances in Mathematics (2011
Effects of liquid and vapor cesium on structural materials
Literature survey on corrosive effects of liquid and vapor cesium on structural materials, and compatibility of cesium as working fluid for Rankine cycle space power plan
Alternator and voltage regulator-exciter for a Brayton cycle space power system. Volume 1 - Design and development
Alternator and voltage regulator for Brayton cycle space power syste
On the homology of locally finite graphs
We show that the topological cycle space of a locally finite graph is a
canonical quotient of the first singular homology group of its Freudenthal
compactification, and we characterize the graphs for which the two coincide. We
construct a new singular-type homology for non-compact spaces with ends, which
in dimension~1 captures precisely the topological cycle space of graphs but
works in any dimension.Comment: 30 pages. This is an extended version of the paper "The homology of a
locally finite graph with ends" (to appear in Combinatorica) by the same
authors. It differs from that paper only in that it offers proofs for Lemmas
3, 4 and 10, as well as a new footnote in Section
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