Sharif Digital Repository

A weighted graph Gω consists of a simple graph G with a weight ω, which is a mapping, ω: E(G)→Z∖{0}. A signed graph is a graph whose edges are labelled with −1 or 1. In this paper, we characterize graphs which have a sign such that their signed adjacency matrix has full rank, and graphs which have a weight such that their weighted adjacency matrix does not have full rank. We show that for any arbitrary simple graph G, there is a sign σ so that Gσ has full rank if and only if G has a {1,2}-factor. We also show that for a graph G, there is a weight ω so that Gω does not have full rank if and only if G has at least two {1,2}-factors. © 2020 Elsevier B.V  

Improving testability during the early stages of High-Level Synthesis (HLS) has several benefits, including reduced test hardware overhead, reduced test costs, reduced design iteration, and significant improved fault coverage. In this paper, we present a novel register allocation method, which is based on weighted graph coloring algorithm, targeting testability improvement for digital circuits. The topics covered in this paper include an overview of HLS and testability parameters, our testability model and experimental results  

In this paper, we present sufficient conditions to address a larger class of digraphs, including balanced ones, whose members' Laplacian (L) makes L 1L + LTL1 to be positive semi-definite, where L1 is the Laplacian associated with a fully connected equally-edged weighted graphs. This property can be later utilized to introduce an appropriate energy function for stability analysis of flocking algorithms in a larger class of networks with switching directed information flow. Also, some of their properties are investigated in the line of matrix theory and graph theory  

The Minimum Maximum Outdegree Problem (MMO) is to assign a direction to every edge in an input undirected, edge-weighted graph so that the maximum weighted outdegree taken over all vertices becomes as small as possible. In this paper, we introduce a new variant of MMO called the p-Split Minimum Maximum Outdegree Problem (p-Split-MMO) in which one is allowed to perform a sequence of p split operations on the vertices before orienting the edges, for some specified non-negative integer p, and study its computational complexity. © 2020 Elsevier B.V  

Improving testability during the early stages of high-level synthesis has several benefits including reduced test hardware overheads, reduced test costs, reduced design iterations, and significant improved fault coverage. In this paper, we present a novel register allocation method, which is based on weighted graph coloring algorithm, targeting testability improvement for digital circuits. In our register allocation method, several high-level testability parameters including sequential depth, sequential loop, and controllability/observability are considered. Our experiments show using this register allocation method results in significant improvement in automatic test pattern generation time... 

Today, public awareness about the benefits of using ontologies in information processing and the semantic web has increased. Since ontologies are useful in various applications, many large ontologies have been developed so far. But various areas like publication, maintenance, validation, processing, and security policies need further research. One way to better tackle these areas is to partition large ontologies into sub partitions. In this paper, we present a new method to partition large ontologies. For the proposed method, three steps are required: (1) transforming an ontology to a weighted graph, (2) partitioning the graph with an algorithm which recognizes the most important concepts,... 

The Minimum Maximum Outdegree Problem (MMO) is to assign a direction to every edge in an input undirected, edge-weighted graph so that the maximum weighted outdegree taken over all vertices becomes as small as possible. In this paper, we introduce a new variant of MMO called the p-Split Minimum Maximum Outdegree Problem (p-Split-MMO) in which one is allowed to perform a sequence of p split operations on the vertices before orienting the edges, for some specified non-negative integer p, and study its computational complexity. © 2018, Springer International Publishing AG, part of Springer Nature  

By the advances in location-aware applications over the Internet, the need for information such as the geographical position of routers and hosts and also the Euclidian distance of nodes is more important than ever. These kinds of information can also provide a valuable insight for network administrators, analysts, and many others. In this paper, we propose an algorithm, called GPE, to estimate the geographical position of nodes across the Internet. In the proposed approach, Internet topology is modeled by a weighted graph. Each node of the graph may have a corresponding estimation of its position. Weight of each edge, in this graph, indicates the estimated length of corresponding link in... 

We propose a novel method for the clustering of point-cloud data that originate from single-molecule localization microscopy (SMLM). Our scheme has the ability to infer a hierarchical structure from the data. It takes a particular relevance when quantitatively analyzing the biological particles of interest at different scales. It assumes a prior neither on the shape of particles nor on the background noise. Our multiscale clustering pipeline is built upon graph theory. At each scale, we first construct a weighted graph that represents the SMLM data. Next, we find clusters using spectral clustering. We then use the output of this clustering algorithm to build the graph in the next scale; in... 

Given a weighted graph G=(V,E) with weight functions c:E→R+ and π:V→R+, and a subset U⊆V, the normalized cut value for U is defined as the sum of the weights of edges exiting U divided by the weight of vertices in U. The mean isoperimetry problem, ISO1(G,k), for a weighted graph G is a generalization of the classical uniform sparsest cut problem in which, given a parameter k, the objective is to find k disjoint nonempty subsets of V minimizing the average normalized cut value of the parts. The robust version of the problem seeks an optimizer where the number of vertices that fall out of the subpartition is bounded by some given integer 0≤ρ≤|V|. The problem may also be considered as the... 

We study the optimal pricing strategy for profit maximization in presence of network externalities where a decision to buy a product depends on the price offered to the buyer and also on the set of her friends who have already bought that product. We model the network influences by a weighted graph where the utility of each buyer is the sum of her initial value on the product, and the linearly additive influence from her friends. We assume that the buyers arrive online and the seller should offer a price to each buyer when she enters the market. We also take into account the manufacturing cost. In this paper, we first assume that the monopolist defines a unique price for the product and... 

Sensor networks are increasingly employed in many applications ranging from environmental to military cases. The network topology used in many sensor network applications has a kind of geographical structure. A graph weighting method for reducing consensus time in random geographical networks is proposed in this paper. We consider a method based on the mutually coupled oscillators for providing general consensus in the network. In this way, one can relate the consensus time to the properties of the Laplacian matrix of the connection graph, i.e. to the second smallest eigenvalue (algebraic connectivity). Our weighting algorithm is based on the node and edge between centrality measures. The...