We present quantum algorithms for the following graph problems: finding a maximal bipartite matching in time O(n √ m + n log n), finding a maximal non-bipartite matching in time O(n( √ m/n+ log n) log n), and finding a maximal flow in an integer network in time O(min(n √ m · U, √ nUm) log n), where n is the number of vertices, m is the number of edges, and U ≤ n is an upper bound on the capacit...

The branching process (BP) approach has been successful in explaining the avalanche dynamics in complex networks. However, its applications are mainly focused on unipartite networks, in which all nodes are of the same type. Here, motivated by a need to understand avalanche dynamics in metabolic networks, we extend the BP approach to a particular bipartite network composed of Boolean AND and OR ...

1 E. coli bipartite network representation 2 Supporting Figure S1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Supporting Table S1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Supporting Figure S2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Supporting Figure S3 . ....

‎for a set of non-negative integers~$l$‎, ‎the $l$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $a_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|a_u cap a_v|in l$‎. ‎the bipartite $l$-intersection number is defined similarly when the conditions are considered only for the ver...

Wireless sensor networks are commonly used to monitor various environmental conditions. Possible geometries for the region covered by a sensor include disks, wedges, and rays, among others, depending on the function of the sensor. In this paper we consider a network consisting of ray sensors deployed to detect intruders traversing a path, not necessarily straight, from a source α to a destinati...

A recurrent 2-dimensional (double) sequence t(m,n) is given by fixing particular sequences t(m, 0), t(0, n) as initial conditions and a rule of recurrence t(m,n) = t(a(m,n − 1), t(m − 1, n − 1), t(m − 1, n)) for m,n ≥ 1. We display such a sequence with values in the set {0, 1} and show that all rows are periodic and that the minimal period of the n-th row has length 2. We conclude that this 2-d...

The Location-Based Social Networks (LBSN) (e.g., Facebook, etc.) have many factors (for instance, ratings, check-in time, location coordinates, reviews etc.) that play a crucial role for the Point-of-Interest (POI) recommendations. Unlike ratings, the reviews can help users to elaborate their opinion and share the extent of consumption experience in terms of the relevant factors of interest (as...

Information on any given topic is often scattered across the Web. Previously this scatter has been characterized through the inequality of distribution of facts (i.e. pieces of information) across webpages. Such an approach conceals how specific facts (e.g. rare facts) occur in specific types of pages (e.g. fact-rich pages). To reveal such regularities, we construct bipartite networks, consisti...

Information on any given topic is often scattered across the Web. Previously this scatter has been characterized through the inequality of distribution of facts (i.e. pieces of information) across webpages. Such an approach conceals how specific facts (e.g. rare facts) occur in specific types of pages (e.g. fact-rich pages). To reveal such regularities, we construct bipartite networks, consisti...

In this paper, subgraphs and complementary graphs are used to analyze the network synchronizability. Some sharp and attainable bounds are provided for the eigenratio of the network structural matrix, which characterizes the network synchronizability, especially when the network’s corresponding graph has cycles, chains, bipartite graphs or product graphs as its subgraphs.