16 research outputs found
Minimum rank and zero forcing number for butterfly networks
The minimum rank of a simple graph is the smallest possible rank over all
symmetric real matrices whose nonzero off-diagonal entries correspond to
the edges of . Using the zero forcing number, we prove that the minimum rank
of the butterfly network is and
that this is equal to the rank of its adjacency matrix
Clearing Contamination in Large Networks
In this work, we study the problem of clearing contamination spreading
through a large network where we model the problem as a graph searching game.
The problem can be summarized as constructing a search strategy that will leave
the graph clear of any contamination at the end of the searching process in as
few steps as possible. We show that this problem is NP-hard even on directed
acyclic graphs and provide an efficient approximation algorithm. We
experimentally observe the performance of our approximation algorithm in
relation to the lower bound on several large online networks including
Slashdot, Epinions and Twitter. The experiments reveal that in most cases our
algorithm performs near optimally
LNCS
The notion of treewidth of graphs has been exploited for faster algorithms for several problems arising in verification and program analysis. Moreover, various notions of balanced tree decompositions have been used for improved algorithms supporting dynamic updates and analysis of concurrent programs. In this work, we present a tool for constructing tree-decompositions of CFGs obtained from Java methods, which is implemented as an extension to the widely used Soot framework. The experimental results show that our implementation on real-world Java benchmarks is very efficient. Our tool also provides the first implementation for balancing tree-decompositions. In summary, we present the first tool support for exploiting treewidth in the static analysis problems on Java programs
Contraction Obstructions for Connected Graph Searching
We consider the connected variant of the classic mixed search game where, in
each search step, cleaned edges form a connected subgraph. We consider graph
classes with bounded connected (and monotone) mixed search number and we deal
with the question whether the obstruction set, with respect of the contraction
partial ordering, for those classes is finite. In general, there is no
guarantee that those sets are finite, as graphs are not well quasi ordered
under the contraction partial ordering relation.
In this paper we provide the obstruction set for , where is the
number of searchers we are allowed to use. This set is finite, it consists of
177 graphs and completely characterises the graphs with connected (and
monotone) mixed search number at most 2. Our proof reveals that the "sense of
direction" of an optimal search searching is important for connected search
which is in contrast to the unconnected original case. We also give a double
exponential lower bound on the size of the obstruction set for the classes
where this set is finite