1,990 research outputs found
Paired 2-disjoint path covers of burnt pancake graphs with faulty elements
The burnt pancake graph is the Cayley graph of the hyperoctahedral
group using prefix reversals as generators. Let and be any
two pairs of distinct vertices of for . We show that there are
and paths whose vertices partition the vertex set of even if
has up to faulty elements. On the other hand, for every
there is a set of faulty edges or faulty vertices for which such a
fault-free disjoint path cover does not exist.Comment: 14 pages, 4 figure
Quantifying fault recovery in multiprocessor systems
Various aspects of reliable computing are formalized and quantified with emphasis on efficient fault recovery. The mathematical model which proves to be most appropriate is provided by the theory of graphs. New measures for fault recovery are developed and the value of elements of the fault recovery vector are observed to depend not only on the computation graph H and the architecture graph G, but also on the specific location of a fault. In the examples, a hypercube is chosen as a representative of parallel computer architecture, and a pipeline as a typical configuration for program execution. Dependability qualities of such a system is defined with or without a fault. These qualities are determined by the resiliency triple defined by three parameters: multiplicity, robustness, and configurability. Parameters for measuring the recovery effectiveness are also introduced in terms of distance, time, and the number of new, used, and moved nodes and edges
Finding paths in sparse random graphs requires many queries
We discuss a new algorithmic type of problem in random graphs studying the
minimum number of queries one has to ask about adjacency between pairs of
vertices of a random graph in order to find a
subgraph which possesses some target property with high probability. In this
paper we focus on finding long paths in when
for some fixed constant . This
random graph is known to have typically linearly long paths.
To have edges with high probability in one
clearly needs to query at least pairs of
vertices. Can we find a path of length economically, i.e., by querying
roughly that many pairs? We argue that this is not possible and one needs to
query significantly more pairs. We prove that any randomised algorithm which
finds a path of length
with at least constant probability in with
must query at least
pairs of vertices. This is
tight up to the factor.Comment: 14 page
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