Papers by Hassan Rezapour
SpringerPlus, 2016
Background The maximum capacity path (MCP) problem is to find a path between two vertices such th... more Background The maximum capacity path (MCP) problem is to find a path between two vertices such that the capacity of the path is maximized, where the capacity of a path is defined as the minimum of the capacities of the arcs and vertices on this path. If waiting times at vertices are not allowable, then the capacity of a path is defined as the minimum of the capacities of the arcs. The MCP problem was introduced by Pollack (1960). He applied the cubic shortest path algorithm to solve this problem. The MCP in undirected graphs was surveyed by Hu (1961). He proposed an algorithm in O(n 2) time by simply taking the paths in a maximum spanning tree. We encourage the reader to study Lawler (1976),
Abstract. Time-varying network optimization problems have tradition-ally been solved by specializ... more Abstract. Time-varying network optimization problems have tradition-ally been solved by specialized algorithms. These algorithms have NP-complement time complexity. This paper considers the time-varying short-est path problem, in which can be optimally solved in O(T(m + n)) time,where T is a given integer. For this problem with arbitrary waiting times,we propose an approximation algorithm, which can solve the problem withO(T(m+n)/ k ) time complexity such that evaluates only a subset of the valuesfor t = {0, 1, . . . , T}.
This paper considers minimum cost flow problem in dynamic networks with uncertain costs. First, w... more This paper considers minimum cost flow problem in dynamic networks with uncertain costs. First, we present a short introduction of dynamic minimum cost flow. Then, we survey discrete and continuous dynamic minimum cost flow problems, their properties and relationships between them. After that, the minimum cost flow problem in discrete dynamic network with uncertainty in the cost vector is considered such that the arc cost can be changed within an interval. Finally, we propose an algorithm to find the optimal solution of the proposed model.
Time-varying network optimization problem, which is NP-complete in the ordinary sense, are tradit... more Time-varying network optimization problem, which is NP-complete in the ordinary sense, are traditionally solved by specialized algorithms. This paper considers the time-varying shortest path problem, which can be optimally solved in O ( T (m+n) ) time, where T is a given integer. For this problem with arbitrary waiting times, we propose an approximate algorithm, which can find an acceptable solution of the problem with O (T (m+n) k ) time complexity such that it evaluates only a subset of the values for t ∈ {0, 1, . . . , T}.
Iraqi journal of science, 2020
The topological indices are functions on the graph that do not depend on the labeling of their ve... more The topological indices are functions on the graph that do not depend on the labeling of their vertices. They are used by chemists for studying the properties of chemical compounds. Let  be a simple connected graph. The Hyper-Zagreb index of the graph ,  is defined as  ,where  and  are the degrees of vertex  and , respectively. In this paper, we study the Hyper-Zagreb index and give upper and lower bounds for .
Iranian journal of mathematical chemistry, 2013
Let G be a simple connected graph. The first and second Zagreb indices have been introduced as  ... more Let G be a simple connected graph. The first and second Zagreb indices have been introduced as  vV(G) (v)2 M1(G) degG and M2(G)  uvE(G)degG(u)degG(v) , respectively, where degG v(degG u) is the degree of vertex v (u) . In this paper, we define a new distance-based named Hyperï€Zagreb as e uv E(G) . (v))2 HM(G)     (degG(u)  degG In this paper, the Hyperï€Zagreb index of the Cartesian product, composition, join and disjunction of graphs are computed.
arXiv: Combinatorics, 2018
Applications in chemistry motivated mathematicians to define different topological indices for di... more Applications in chemistry motivated mathematicians to define different topological indices for different types of graphs. The Hyper-Zagreb index (HM) is an important tool as it integrates the first and the second Zagreb indices. In this paper, we characterize the trees and unicyclic graphs with the first four and first eight greatest HM-value, respectively.
In this book, we consider the time-varying shortest path problem with one objective or multi-obje... more In this book, we consider the time-varying shortest path problem with one objective or multi-objectives. In these problems, transit and waiting costs are not necessarily known in each time steps. We survey the time-varying shortest path, regarding to waiting times at vertices. Moreover, the time-varying shortest path problem with arbitrary waiting times at vertices is considered, where transit costs and waiting costs are fuzzy numbers or possibly belong to some intervals. Then, two new algorithms for solving the time-varying shortest path with uncertain costs are proposed. Afterwards, we consider the shortest path problem on a time-varying network with multi-objectives functions to optimize. These K-objectives are associated with K attributes, which cannot combine together. The problem is to find the efficient path P from a source vertex to a target vertex such that the cost of path is minimized, where the total time of path is at most time horizon. Then, the maximum capacity path p...
In this paper, we propose an algorithm for solving the robust time-varying shortest path problem ... more In this paper, we propose an algorithm for solving the robust time-varying shortest path problem in which the waiting time at any vertex is not restricted. The problem is to find the shortest path connecting source node s and sink node i in a timevarying network flow such that the time of the path is at most T , where T is a given integer, the transit costs are uncertain and waiting time is arbitrarily allowed at any of the vertices.
Trends in Applied Sciences Research, 2015
This study considers a k-objective time-varying shortest path problem, which cannot be combined i... more This study considers a k-objective time-varying shortest path problem, which cannot be combined into a single overall objective. In this problem, the transit cost to traverse an arc is varying over time, which depend upon the departure time at the beginning vertex of the arc. An algorithm is presented for finding the efficient solutions of problem and its complexity of algorithm is analyzed. Finally, an illustrative example is also provided to clarify the problem.
In this paper, we focus on the time-varying shortest path problem, where the transit costs are fu... more In this paper, we focus on the time-varying shortest path problem, where the transit costs are fuzzy numbers. Moreover, we consider this problem in which the transit time can be shortened at a fuzzy speedup cost. Speedup may also be a better decision to find the shortest path from a source vertex to a specified vertex.
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Papers by Hassan Rezapour