Sharif Digital Repository

Let G be a graph and let f be a positive integer-valued function on V(G). In this paper, we show that if for all S⊆V(G), ω(G∖S)<∑v∈S(f(v)−2)+2+ω(G[S]), then G has a spanning tree T containing an arbitrary given matching such that for each vertex v, dT(v)≤f(v), where ω(G∖S) denotes the number of components of G∖S and ω(G[S]) denotes the number of components of the induced subgraph G[S] with the vertex set S. This is an improvement of several results. Next, we prove that if for all S⊆V(G), ω(G∖S)≤∑v∈S(f(v)−1)+1, then G admits a spanning closed walk passing through the edges of an arbitrary given matching meeting each vertex v at most f(v) times. This result solves a long-standing conjecture... 

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  

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. © 2020  

This paper proposes a new approach to study the sensitivity analysis in the network flow problems, in particular, the minimum spanning tree and shortest path problems. In a sensitivity analysis, one looks for the amount of changes in the edges’ weights, number of edges or number of vertices such that the optimal solution, i.e., the minimum spanning tree or shortest path does not change. We introduce a novel approach, and develop associated equations and mathematics. We discuss two illustrative examples to show the applicability of the proposed approach. © International Journal of Industrial Engineering  

Liu and Xu (1998) and Ellingham, Nam and Voss (2002) independently showed that every k-edge-connected simple graph G has a spanning tree T such that for each vertex v, dT(v) ≤ ⌈ d(v)/k ⌉ + 2. In this paper we show that every k-edge-connected graph G has a spanning tree T such that for each vertex v, dT(v)≤ ⌈ d(v)-2/k ⌉ + 2; also if G has k edge-disjoint spanning trees, then T can be found such that for each vertex v, dT(v) ≤ ⌈ d(v)-1/k ⌉ + 1. This result implies that every (r-1)-edge-connected r-regular graph (with r ≥ 4) has a spanning Eulerian subgraph whose degrees lie in the set {2,4,6}; also reduces the edge-connectivity needed for some theorems due to Barát and Gerbner (2014) and... 

For a set of n points in the plane, this paper presents simple kinetic data structures (KDSs) for solutions to some fundamental proximity problems, namely, the all nearest neighbors problem, the closest pair problem, and the Euclidean minimum spanning tree (EMST) problem. Also, the paper introduces KDSs for maintenance of two well-studied sparse proximity graphs, the Yao graph and the Semi-Yao graph. We use sparse graph representations, the Pie Delaunay graph and the Equilateral Delaunay graph, to provide new solutions for the proximity problems. Then we design KDSs that efficiently maintain these sparse graphs on a set of n moving points, where the trajectory of each point is assumed to be... 

In this paper, we propose and analyze flocking algorithms in a network of second-order agents with bounded control inputs and nonlinear intrinsic dynamics. We consider a general switching network topology, for velocity information exchange, rather than undirected or fixed directed network topology with a directed spanning tree. The proposed adaptive controller architecture applies a leader-following strategy in which the pinning scheme is defined based on the interaction topology. Finally, some examples are presented to illustrate the theoretical results  

We design an optimal pipe diameter sizing in a tree-structured natural gas network. Design of pipeline, facility and equipment systems are necessary tasks to configure an optimal natural gas network. A mixed-integer programming model is formulated to minimise the total cost in the network. The aim is to optimise pipe diameter sizes so that the location-allocation cost is minimised. Pipeline systems in natural gas network must be designed based on gas flow rate, length of pipe, gas maximum drop pressure allowance and gas maximum velocity allowance. We use information based on relationship among gas flow rates and pipe diameter sizes considering gas pressure and velocity restrictions. We apply... 

This paper presents a kinetic data structure (KDS) for maintenance of the Euclidean minimum spanning tree (EMST) on a set of moving points in 2-dimensional space. For a set of n points moving in the plane we build a KDS of size O(n) in O(nlogn) preprocessing time by which the EMST is maintained efficiently during the motion. This is done by applying the required changes to the combinatorial structure of the EMST which is changed in discrete timestamps. We assume that the motion of the points, i.e. x and y coordinates of the points, are defined by algebraic functions of constant maximum degree. In terms of the KDS performance parameters, our KDS is responsive, local, and compact. The... 

We construct a new proximity graph, called the Pie Delaunay graph, on a set of n points which is a super graph of Yao graph and Euclidean minimum spanning tree (EMST). We efficiently maintain the Pie Delaunay graph where the points are moving in the plane. We use the kinetic Pie Delaunay graph to create a kinetic data structure (KDS) for maintenance of the Yao graph and the EMST on a set of n moving points in 2-dimensional space. Assuming x and y coordinates of the points are defined by algebraic functions of at most degree s, the structure uses O(n) space, O(nlogn) preprocessing time, and processes O(n 2 λ 2s∈+∈2(n)β s + 2(n)) events for the Yao graph and O(n 2 λ 2s + 2(n)) events for the... 

An Ant Colony Optimization (ACO) algorithm is proposed for optimal tree-structured natural gas distribution network. Design of pipelines, facilities, and equipment systems are necessary tasks to configure an optimal natural gas network. A mixed integer programming model is formulated to minimize the total cost in the network. The aim is to optimize pipe diameter sizes so that the location-allocation cost is minimized. Pipeline systems in natural gas network must be designed based on gas flow rate, length of pipe, gas maximum pressure drop allowance, and gas maximum velocity allowance. We use the information regarding gas flow rates and pipe diameter sizes considering the gas pressure and... 

This paper presents the first kinetic data structure (KDS) for maintenance of the Euclidean minimum spanning tree (EMST) on a set of n moving points in 2-dimensional space. We build a KDS of size O(n) in O(nlogn) preprocessing time by which their EMST is maintained efficiently during the motion. In terms of the KDS performance parameters, our KDS is responsive, local, and compact  

There are many practical situations where it is desirable or even required to achieve stable convergence in the finite-time domain. In this paper, a simple distributed continuous-time protocol is introduced that guarantees finite-time consensus in networks of autonomous agents. Protocol convergence in weighted directed/undirected and fixed/switching networks is explored based on a Lyapunov analysis. The stability of the system and the solvability of the consensus algorithm are proved for network topologies that contain a spanning tree frequently enough over contiguous time intervals. The decision value for different topologies and for multi-rate integrator agents is investigated, and a novel... 

Here, a case study of natural gas network is conducted. We design an optimal distribution network of natural gas. Our proposed network is composed of stations reducing gas pressure to desirable pressure using consumer's viewpoint. By using minimum spanning tree (MST) technique, an optimal distribution network among stations and consumers is constructed. Our aim is to determine both locations and types of stations minimizing location-allocation costs in the network. A case study in Mazandaran Gas Company in Iran is made to assess the validity and effectiveness of the proposed model  

In this paper, we enumerate the number of combinatorial changes of the the Euclidean minimum spanning tree (EMST) of a set of n moving points in 2- dimensional space. We assume that the motion of the points in the plane, is defined by algebraic functions of maximum degree s of time. We prove an upper bound of O(n3β2s(n2)) for the number of the combinatorial changes of the EMST, where βs(n)= λs(n)/n and λs(n) is the maximum length of Davenport-Schinzel sequences of order s on n symbols which is nearly linear in n. This result is an O(n) improvement over the previously trivial bound of O(n4)  

We consider the design of an optimal natural-gas network. Our proposed network contains two echelons, Town Broad Stations (TBSs), and consumers (demand zones). Here, our aim is a two-stage cost minimization. We first determine locations of the TBS so that the location-allocation cost is minimized. Then, we show how to distribute the flow of gas among the TBS minimizing the flow cost by using Minimum Spanning Tree (MST). A case study in Mazandaran Gas Company in Iran is made to assess the validity and effectiveness of our proposed model  

In this paper, we consider the problem of searching a network for intruders. We propose a strategy for capturing the intruder in the popular interconnection topology, the star network. According to the proposed strategy, a team of collaborative software agents are responsible for capturing a hostile intruder (e.g. a virus). These agents asynchronously move along the network links and the intruder has the capability of escaping arbitrarily fast. © 2009 IEEE  

In this paper, we will discuss two special classes of mathematical programming models with fuzzy random variables. In the first model, a linear programming problem with fuzzy decision variables and fuzzy random coefficients is introduced. Then an algorithm is developed to solve the model based on fuzzy optimization method and fuzzy ranking method. In the second model, a fuzzy random quadratic spanning tree problem is presented. Then the proposed problem is formulated and solved by using the scalar expected value of fuzzy random variables. Furthermore, illustrative numerical examples are also given to clarify the methods discussed in this paper  

Given an undirected graph with weights associated with its edges, the Steiner tree problem consists of finding a minimum weight subtree spanning a given subset of (terminal) nodes of the original graph. Minimum Spanning Tree Heuristic (MSTH) is a heuristic for solving the Steiner problem in graphs. In this paper we first review existing algorithms for solving the Steiner problem in graphs. We then introduce a new parallel version of MSTH on three dimensional mesh of trees architecture. We describe our algorithm and analyze its time complexity. The time complexity analysis shows that the algorithm's running time is O(lg2 n) which is comparable with other existing parallel solutions. © 2007...