Sharif Digital Repository

Given a metric graph G, we are concerned with finding a spanning tree of G where the maximum weighted degree of its vertices is minimum. In a metric graph (or its spanning tree), the weighted degree of a vertex is defined as the sum of the weights of its incident edges. In this paper, we propose a 4.5-approximation algorithm for this problem. We also prove it is NP-hard to approximate this problem within a 2 - ε factor. © 2007 Elsevier B.V. All rights reserved  

A multicolored tree is a tree whose edges have different colors. Brualdi and Hollingsworth [5] proved in any proper edge coloring of the complete graph K2n(n > 2) with 2n -1 colors, there are two edge-disjoint multicolored spanning trees. In this paper we generalize this result showing that if (a1,..., ak) is a color distribution for the complete graph Kn, n ≥ 5, such that 2 ≤ a1 ≤ a2 ≤ ⋯ ≤ ak ≤ (n + 1)/2, then there exist two edge-disjoint multicolored spanning trees. Moreover, we prove that for any edge coloring of the complete graph Kn with the above distribution if T is a non-star multicolored spanning tree of Kn, then there exists a multicolored spanning tree T′ of Kn such that T and T′... 

In this paper, we show that by considering the factor of usage in instruction bundles in VLIW processors and using the slots filled with NOPs in bundles, we can improve the overall performance by reducing the total execution time of the program. By our proposed scheme, Combined Bundle Scheduling (CBS), we have gained better performance compared to that for the PDT scheme (Predicted Decision Tree scheduling) which is the best scheduling strategy known so far. © 2006 IEEE  

In this article we show that for any forest there exists a labelling of the vertices for which the row-reduced echelon form of its adjacency matrix is a {-1, 0, 1}-matrix. This result clearly provides an affirmative answer to the conjecture: The null space of the adjacency matrix of every forest has a {-1, 0, 1}-basis. © 2005 Elsevier Inc. All rights reserved  

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... 

Let G be a graph and for any natural number r, χs ′ (G, r) denotes the minimum number of colors required for a proper edge coloring of G in which no two vertices with distance at most r are incident to edges colored with the same set of colors. In [Z. Zhang, L. Liu, J. Wang, Adjacent strong edge coloring of graphs, Appl. Math. Lett. 15 (2002) 623-626] it has been proved that for any tree T with at least three vertices, χs ′ (T, 1) ≤ Δ (T) + 1. Here we generalize this result and show that χs ′ (T, 2) ≤ Δ (T) + 1. Moreover, we show that if for any two vertices u and v with maximum degree d (u, v) ≥ 3, then χs ′ (T, 2) = Δ (T). Also for any tree T with Δ (T) ≥ 3 we prove that χs ′ (T, 3) ≤ 2 Δ... 

Hoffmann–Ostenhof's conjecture states that the edge set of every connected cubic graph can be decomposed into a spanning tree, a matching and a 2-regular subgraph. In this paper, we show that the conjecture holds for claw-free subcubic graphs and 4-chordal subcubic graphs. © 2021 Elsevier B.V  

Hoffmann–Ostenhof's conjecture states that the edge set of every connected cubic graph can be decomposed into a spanning tree, a matching and a 2-regular subgraph. In this paper, we show that the conjecture holds for claw-free subcubic graphs and 4-chordal subcubic graphs. © 2021 Elsevier B.V  

In this paper, a diverse range of routing algorithms is classified into a new family of routings called zone-ordered label-based routing algorithms. The proposed classification is based on three common steps (factors) for generating such routings, namely, graph labeling, deadlock-free zones, and zone ordering. The main goal of this classification is to define several new routing concepts and streamline the knowledge on routing algorithms. Following the classification, a novel methodology is proposed to generate routing algorithms for irregular networks. The methodology uses the three mentioned steps to generate deadlock-free routings. Consequently, the methodology-based routings fall into... 

We consider the problem of walking in an unknown street, starting from a point s, to reach a target t by a robot which has a minimal sensing capability. The goal is to decrease the traversed path as short as possible. The robot cannot infer any geometric properties of the environment such as coordinates, angles or distances. The robot is equipped with a sensor that can only detect the discontinuities in the depth information (gaps) and can locate the target point as soon as it enters in its visibility region. In addition, a pebble as an identifiable point is available to the robot to mark some position of the street. We offer a data structure similar to Gap Navigation Tree to maintain the... 

This paper is aimed at investigating some computational aspects of different isoperimetric problems on weighted trees. In this regard, we consider different connectivity parameters called minimum normalized cuts/isoperimetric numbers defined through taking the minimum of the maximum or the mean of the normalized outgoing flows from a set of subdomains of vertices, where these subdomains constitute a partition/subpartition. We show that the decision problem for the case of taking k-partitions and the maximum (called the max normalized cut problem NCPM), and the other two decision problems for the mean version (referred to as IPPm and NCPm) are NP-complete problems for weighted trees. On the... 

In this paper, a diverse range of routing algorithms is classified into a new family of routings called zone-ordered label-based routing algorithms. The proposed classification is based on three common steps (factors) for generating such routings, namely, graph labeling, deadlock-free zones, and zone ordering. The main goal of this classification is to define several new routing concepts and streamline the knowledge on routing algorithms. Following the classification, a novel methodology is proposed to generate routing algorithms for irregular networks. The methodology uses the three mentioned steps to generate deadlock-free routings. Consequently, the methodology-based routings fall into... 

We consider an interacting system of spin variables on a loopy interaction graph, identified by a tree graph and a set of loopy interactions. We start from a high-temperature expansion for loopy interactions represented by a sum of non-negative contributions from all the possible frustration-free loop configurations. We then compute the loop corrections using different approximations for the nonlocal loop interactions induced by the spin correlations in the tree graph. For distant loopy interactions, we can exploit the exponential decay of correlations in the tree interaction graph to compute loop corrections within an independent-loop approximation. Higher orders of the approximation are... 

Due to complicated implementation of IP multicast, application layer multicast has attracted the attention of researchers. Tree overlay has some challenges such as resiliency problems caused by peer churns and also network resources may not be efficiently used. Mesh overlay doesn't have such problems, but has a high delivery latency and overhead caused by pull mechanism. Using a hybrid mesh/tree overlay offers push pull approach and leads to use the advantages of both overlays simultaneously. Also in p2p networks a significant problem is heterogeneity of peers. In this paper we propose a hybrid mesh/tree overlay that by means of streaming layered coded video, addresses these challenges. This... 

A universal labeling of a graph G is a labeling of the edge set in G such that in every orientation ℓ 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 { 1 , 2 , … , k} denoted it by χu→ (G). We have 2 Δ (G) - 2 ≤ χu→ (G) ≤ 2 Δ ( G ), where Δ (G) 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, χu→ (G) ≤ f(Δ (G)) ?”. Towards this question, we introduce some lower and upper bounds on their parameter... 

“How many guards are required to cover an art gallery?” asked Victor Klee in 1973, initiated a deep and interesting research area in computational geometry. This problem, referred to as the Art Gallery Problem, has been considered thoroughly in the literature. A recent version of this problem, introduced by Sadhu et al. in CCCG'10, is related to the connectivity of the guards. In this version, for a given set of initial guards inside a given simple polygon, the goal is to obtain a minimum set of new guards, such that the new guards alongside the initial ones have a connected visibility graph. The visibility graph of a set of points inside a simple polygon is a graph whose vertices correspond... 

Peer to Peer networks have received considerable attention during the past decade and have been the focus of many research and development activities. New applications such as video streaming or gaming would benefit from multicast topologies and creating such trees in peer to peer networks is a challenging task. Proper multicast trees should minimize the traffic delay and bandwidth consumption. At the same time, construction of these trees should not be very complicated in terms of the required processing power so they can be implemented easily. The required time for construction of multicast trees should also be minimized and that helps with their adaptation to the dynamics of the network.... 

Determining the capacity of watermark for images is a complex task. This capacity may be influenced by many factors such as the content of image and also the strength of watermark. In some recent works the image content has been considered for calculation of watermark capacity. One such approach is to use the Noise Visibility Function (NVF) introduced in [3]. In this paper we introduced a new method for finding NVF according to the quad tree representation of image instead of using pixel neighborhood data. Our experimental results showed that the depth of a pixel in image quad tree represents much information about the pixel and its maximum allowable distortion compared to pixel neighborhood... 

This paper presents the SkipTree, a new balanced, distributed data structure for storing data with multidimensional keys in a peer-to-peer network. The SkipTree supports range queries as well as single point queries which are routed in O(log n) hops. SkipTree is fully decentralized with each node being connected to O(logn) other nodes. The memory usage for maintaining the links at each node is O(log n log log n) on average and O(log2 n) in the worst case. Load balance is also guaranteed to be within a constant factor. © Springer-Verlag Berlin Heidelberg 2005  

A hybrid video codec, where the intraframe pictures are wavelet-based coded and the interframe pictures are coded with a standard H.263 codec is proposed. We show that intraframe-wavelet coded pictures not only improve the quality of I-pictures but also result in lower distorted prediction pictures that outperforms a pure H.263 video codec. © 2005 IEEE