Sharif Digital Repository

Improving testability during the early stages of High-Level Synthesis (HLS) reduces test hardware overheads, test costs, design iterations, and also improves fault coverage. In this paper, we present a novel register allocation algorithm which is based on weighted graph coloring, targeting testability improvement. © 2003 IEEE  

We study the asymptotic behavior of the capacity of erasure networks under a restricted class of network coding schemes, called spatial network coding. In spatial network coding, nodes are permitted to only combine data units received from distinct incoming links; multiple data units arriving on the same link may not be coded together. Elsewhere, it has been shown that the network capacity under spatial network coding is the statistical mean of the minimum cut value. In this paper, we come up with a new concept in the random graph theory referred to as typical min-cut family, which parallels the information theoretic notion of typical sequences, and use it to develop an analytical tool for... 

Diffusion of key schedule algorithm plays an important role in security of block ciphers. In this paper, we present a new approach to key schedule diffusion analysis by taking the advantages of graph theory modeling. This modeling can help to disclose the weaknesses of key schedules. In this line, the key schedule weaknesses of Twine-128 are shown and an improved key schedule is proposed. In order to make a fair comparison, some parameters are introduced to quantify the diffusion property of key schedule, and compare the results for Twine-128 with both key schedules. The results show that the new key schedule made Twine-128 stronger. Also for more reliability, the results of biclique attack... 

Recent progress in the areas of network science and control has shown a significant promise in understanding and analyzing epidemic processes. A well-known model to study epidemics processes used by both control and epidemiological research communities is the susceptible–infected–susceptible (SIS) dynamics to model the spread of disease/viruses over contact networks of infected and susceptible individuals. The SIS model has two metastable equilibria: one is called the endemic equilibrium and the other is known as the disease-free or healthy-state equilibrium. Control theory provides the tools to design control actions (allocating curing or vaccination resources) in order to achieve and... 

In this paper we define critical graphs as minimal graphs that support a given set of rates for the index coding problem, and study them for both the one-shot and asymptotic setups. For the case of equal rates, we find the critical graph with minimum number of edges for both one-shot and asymptotic cases. For the general case of possibly distinct rates, we show that for one-shot and asymptotic linear index coding, as well as asymptotic non-linear index coding, each critical graph is a union of disjoint strongly connected subgraphs (USCS). On the other hand, we identify a non-USCS critical graph for a one-shot non-linear index coding problem. In addition, we show that the capacity region of... 

We revisit the problem of finding k paths with a minimum number of shared edges between two vertices of a graph. An edge is called shared if it is used in more than one of the k paths. We provide a ⌊k/2⌋-approximation algorithm for this problem, improving the best previous approximation factor of k - 1. We also provide the first approximation algorithm for the problem with a sublinear approximation factor of O(n3/4), where n is the number of vertices in the input graph. For sparse graphs, such as bounded-degree and planar graphs, we show that the approximation factor of our algorithm can be improved to O(√n). While the problem is NP-hard, and even hard to approximate to within an O(log n)... 

Let R be a ring and X R be a non-empty set. The regular graph of X, Γ(X), is defined to be the graph with regular elements of X (non-zero divisors of X) as the set of vertices and two vertices are adjacent if their sum is a zero divisor. There is an interesting question posed in BCC22. For a field F, is the chromatic number of Γ( GLn(F)) finite? In this paper, we show that if G is a soluble subgroup of GLn(F), then χ(Γ(G))<∞. Also, we show that for every field F, χ(Γ( Mn(F)))=χ(Γ( Mn(F(x)))), where x is an indeterminate. Finally, for every algebraically closed field F, we determine the maximum value of the clique number of Γ(), where denotes the subgroup generated by A∈ GLn(F)  

A lucky labeling of a graph G is a function l:V(G)→N, such that for every two adjacent vertices v and u of G, σ w∼vl(w)≠ σ w∼ul(w) (x∼y means that x is joined to y). A lucky number of G, denoted by η(G), is the minimum number k such that G has a lucky labeling l:V(G)→{1,⋯,k}. We prove that for a given planar 3-colorable graph G determining whether η(G)=2 is NP-complete. Also for every k≥2, it is NP-complete to decide whether η(G)=k for a given graph G  

In this paper, we consider the following problem: given an undirected graph G=(V,E) and an integer k, find I⊆V2 with |I|≤k in such a way that G'=(V,E∪I) has the maximum number of triangles (a cycle of length 3). We first prove that this problem is NP-hard and then give an approximation algorithm for it  

A universal labeling of a graph G is a labeling of the edge set in G such that in every orientation (Formula presented.) of G for every two adjacent vertices v and u, the sum of incoming edges of v and u in the oriented graph are different from each other. The universal labeling number of a graph G is the minimum number k such that G has universal labeling from (Formula presented.) denoted it by (Formula presented.). We have (Formula presented.), where (Formula presented.) denotes the maximum degree of G. In this work, we offer a provocative question that is: “Is there any polynomial function f such that for every graph G, (Formula presented.)?”. Towards this question, we introduce some... 

Clustering is a major task in data mining which is used in many applications. However, general clustering is inappropriate for many applications where some constraints should be applied. One category of these constraints is the cluster size constraint. In this paper, we propose a new algorithm for solving the clustering with balancing constraints by using the minimum matching. We compare our algorithm with the method proposed by Banerjee and Ghosh that uses stable matching and show that our algorithm converge to the final solution in fewer iterations. ©2009 IEEE  

We say that two graphs G1 and G2 with the same vertex set commute if their adjacency matrices commute. In this paper, we find all integers n such that the complete bipartite graph Kn, n is decomposable into commuting perfect matchings or commuting Hamilton cycles. We show that there are at most n - 1 linearly independent commuting adjacency matrices of size n; and if this bound occurs, then there exists a Hadamard matrix of order n. Finally, we determine the centralizers of some families of graphs. © 2008 Elsevier B.V. All rights reserved  

In this paper, using the chromatic properties of power graphs we propose a new approach for placing resources in symmetric networks. Our novel placement scheme guarantees a perfect placement when such a solution is feasible in the topology, while in general it answers the question of k-resource placement at a distance d where each non-resource node is able to access k resource nodes within at most d hops away. We define a quasi-perfect graph as a graph whose clique number and chromatic number are equal. We derive important properties of quasi-perfect graphs and use them to find a solution for the resource placement problem. We have also applied the proposed method to find a distant resource... 

An induced path factor of a graph (Formula presented.) is a set of induced paths in (Formula presented.) with the property that every vertex of (Formula presented.) is in exactly one of the paths. The induced path number (Formula presented.) of (Formula presented.) is the minimum number of paths in an induced path factor of (Formula presented.). We show that if (Formula presented.) is a connected cubic graph on (Formula presented.) vertices, then (Formula presented.). Fix an integer (Formula presented.). For each (Formula presented.), define (Formula presented.) to be the maximum value of (Formula presented.) over all connected (Formula presented.) -regular graphs (Formula presented.) on... 

We introduce two necessary conditions for the existence of graph homomorphisms based on the concepts of density and power graph. As corollaries, we obtain a lower bound for the fractional chromatic number, and we set forward elementary proofs of the facts that the circular chromatic number of the Petersen graph is equal to three and the fact that the Coxeter graph is a core. © 2007 Elsevier B.V. All rights reserved  

A set S of vertices of a graph G = (V, E) with no isolated vertex is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. The total domination numberγt (G) is the minimum cardinality of a total dominating set of G. The total domination subdivision numbersdγt (G) is the minimum number of edges that must be subdivided in order to increase the total domination number. We consider graphs of order n ≥ 4, minimum degree δ and maximum degree Δ. We prove that if each component of G and over(G, -) has order at least 3 and G, over(G, -) ≠ C5, then γt (G) + γt (over(G, -)) ≤ frac(2 n, 3) + 2 and if each component of G and over(G, -) has order at least 2 and at least one...