9,819 research outputs found
RASCAL: calculation of graph similarity using maximum common edge subgraphs
A new graph similarity calculation procedure is introduced for comparing labeled graphs. Given a minimum similarity threshold, the procedure consists of an initial screening process to determine whether it is possible for the measure of similarity between the two graphs to exceed the minimum threshold, followed by a rigorous maximum common edge subgraph (MCES) detection algorithm to compute the exact degree and composition of similarity. The proposed MCES algorithm is based on a maximum clique formulation of the problem and is a significant improvement over other published algorithms. It presents new approaches to both lower and upper bounding as well as vertex selection
On parameterized complexity of the Multi-MCS problem
AbstractWe introduce the maximum common subgraph problem for multiple graphs (Multi-MCS) inspired by various biological applications such as multiple alignments of gene sequences, protein structures, metabolic pathways, or protein–protein interaction networks. Multi-MCS is a generalization of the two-graph Maximum Common Subgraph problem (MCS). On the basis of the framework of parameterized complexity theory, we derive the parameterized complexity of Multi-MCS for various parameters for different classes of graphs. For example, for directed graphs with labeled vertices, we prove that the parameterized m-Multi-MCS problem is W[2]-hard, while the parameterized k-Multi-MCS problem is W[t]-hard (∀t≥1), where m and k are the size of the maximum common subgraph and the number of multiple graphs, respectively. We show similar results for other parameterized versions of the Multi-MCS problem for directed graphs with vertex labels and undirected graphs with vertex and edge labels by giving linear FPT reductions of the problems from parameterized versions of the longest common subsequence problem. Likewise, for unlabeled undirected graphs, we show that a parameterized version of the Multi-MCS problem with a fixed number of input graphs is W[1]-complete by showing a linear FPT reduction to and from a parameterized version of the maximum clique problem
Moving in temporal graphs with very sparse random availability of edges
In this work we consider temporal graphs, i.e. graphs, each edge of which is
assigned a set of discrete time-labels drawn from a set of integers. The labels
of an edge indicate the discrete moments in time at which the edge is
available. We also consider temporal paths in a temporal graph, i.e. paths
whose edges are assigned a strictly increasing sequence of labels. Furthermore,
we assume the uniform case (UNI-CASE), in which every edge of a graph is
assigned exactly one time label from a set of integers and the time labels
assigned to the edges of the graph are chosen randomly and independently, with
the selection following the uniform distribution. We call uniform random
temporal graphs the graphs that satisfy the UNI-CASE. We begin by deriving the
expected number of temporal paths of a given length in the uniform random
temporal clique. We define the term temporal distance of two vertices, which is
the arrival time, i.e. the time-label of the last edge, of the temporal path
that connects those vertices, which has the smallest arrival time amongst all
temporal paths that connect those vertices. We then propose and study two
statistical properties of temporal graphs. One is the maximum expected temporal
distance which is, as the term indicates, the maximum of all expected temporal
distances in the graph. The other one is the temporal diameter which, loosely
speaking, is the expectation of the maximum temporal distance in the graph. We
derive the maximum expected temporal distance of a uniform random temporal star
graph as well as an upper bound on both the maximum expected temporal distance
and the temporal diameter of the normalized version of the uniform random
temporal clique, in which the largest time-label available equals the number of
vertices. Finally, we provide an algorithm that solves an optimization problem
on a specific type of temporal (multi)graphs of two vertices.Comment: 30 page
Algorithms for square-3PC(·, ·)-free Berge graphs
We consider the class of graphs containing no odd hole, no odd antihole, and no configuration consisting of three paths between two nodes such that any two of the paths
induce a hole, and at least two of the paths are of length 2. This class generalizes clawfree Berge graphs and square-free Berge graphs. We give a combinatorial algorithm of
complexity O(n7) to find a clique of maximum weight in such a graph. We also consider several subgraph-detection problems related to this class
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