Bipartite Graphs and their Applications

Parallel desynchronized block matching: A feasible scheduling algorithm for the input-buffered wavelength-routed switch

“…Once delay assignment in a time slot is finished, the state vector for the succeeding time slot should reflect the propagation of the packets across the fiber delay lines, and remove the packets that leave the buffering section. The scheduling problem to be solved in one time slot can be expressed as a type matching problem in a bipartite graph [12]. The graph is constructed as follows: nN left side nodes, one for every input port.…”

“…This algorithm obtains the matching of the maximum size, giving preference to the arcs destined to lower delay nodes, when performing path augmentation [12]. Unfortunately, the complexity of the most efficient algorithm known to date obtaining the optimum MSM solution of an N×N bipartite graph is O(mlog(m)), being m the number of edges [14].…”

An Accurate System-Wide Anonymity Metric for Probabilistic Attacks

“…It is well known (see, for example, Asratian et al [4]) that this number is the same as the permanent of the biadjacency matrix of that graph. The permanent of any n × n matrix M = [m ij ] of real numbers is defined as:…”

“…2(b). Note that in this graph s 1 is connected to only t 1 and t 2 , and not to t 3 or t 4 , since the edges s 1 , t 3 and s 1 , t 4 were determined by the attack to be infeasible. The biadjacency matrix of this graph, a 0-1 matrix with a row for each input message and a column for each output message, is given in Fig.…”

Some voltage graph-based LDPC tailbiting codes with large girth

“…Every full-rank parity-check matrix H of a rate R = k/n LDPC block code can be interpreted as the biadjacency matrix [10] of a bipartite graph, the so-called Tanner graph, having two disjoint subsets V 0 and V 1 containing n and n−k vertices, respectively. The n vertices in V 0 are called symbol nodes, while the n − k vertices in V 1 are called constraint nodes.…”