20 research outputs found
Tight lower bounds on the number of bicliques in false-twin-free graphs
A \emph{biclique} is a maximal bipartite complete induced subgraph of .
Bicliques have been studied in the last years motivated by the large number of
applications. In particular, enumeration of the maximal bicliques has been of
interest in data analysis. Associated with this issue, bounds on the maximum
number of bicliques were given. In this paper we study bounds on the minimun
number of bicliques of a graph. Since adding false-twin vertices to does
not change the number of bicliques, we restrict to false-twin-free graphs. We
give a tight lower bound on the minimum number bicliques for a subclass of
,false-twin-free graphs and for the class of
,false-twin-free graphs. Finally we discuss the problem for general
graphs.Comment: 16 pages, 4 figue
AND-NOT logic framework for steady state analysis of Boolean network models
Finite dynamical systems (e.g. Boolean networks and logical models) have been
used in modeling biological systems to focus attention on the qualitative
features of the system, such as the wiring diagram. Since the analysis of such
systems is hard, it is necessary to focus on subclasses that have the
properties of being general enough for modeling and simple enough for
theoretical analysis. In this paper we propose the class of AND-NOT networks
for modeling biological systems and show that it provides several advantages.
Some of the advantages include: Any finite dynamical system can be written as
an AND-NOT network with similar dynamical properties. There is a one-to-one
correspondence between AND-NOT networks, their wiring diagrams, and their
dynamics. Results about AND-NOT networks can be stated at the wiring diagram
level without losing any information. Results about AND-NOT networks are
applicable to any Boolean network. We apply our results to a Boolean model of
Th-cell differentiation
Efficient Enumeration of Bipartite Subgraphs in Graphs
Subgraph enumeration problems ask to output all subgraphs of an input graph
that belongs to the specified graph class or satisfy the given constraint.
These problems have been widely studied in theoretical computer science. As
far, many efficient enumeration algorithms for the fundamental substructures
such as spanning trees, cycles, and paths, have been developed. This paper
addresses the enumeration problem of bipartite subgraphs. Even though bipartite
graphs are quite fundamental and have numerous applications in both theory and
application, its enumeration algorithms have not been intensively studied, to
the best of our knowledge. We propose the first non-trivial algorithms for
enumerating all bipartite subgraphs in a given graph. As the main results, we
develop two efficient algorithms: the one enumerates all bipartite induced
subgraphs of a graph with degeneracy in time per solution. The other
enumerates all bipartite subgraphs in time per solution
Incremental Maintenance of Maximal Bicliques in a Dynamic Bipartite Graph
We consider incremental maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition of edges. When new edges are added to the graph, we seek to enumerate the change in the set of maximal bicliques, without enumerating the set of maximal bicliques that remain unaffected. The challenge is to enumerate the change without explicitly enumerating the set of all maximal bicliques. In this work, we present (1)~Near-tight bounds on the magnitude of change in the set of maximal bicliques of a graph, due to a change in the edge set, and an (2)~Incremental algorithm for enumerating the change in the set of maximal bicliques. For the case when a constant number of edges are added to the graph, our algorithm is change-sensitive , i.e., its time complexity is proportional to the magnitude of change in the set of maximal bicliques. To our knowledge, this is the first incremental algorithm for enumerating maximal bicliques in a dynamic graph, with a provable performance guarantee. Experimental results show that its performance exceeds that of baseline implementations by orders of magnitude