 # Farzad DidehvarAmirkabir University of Technology | TUS · Department of Mathematics and Computer Science

14.33
·
Phd

64
Publications
7,543
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169
Citations
Introduction

## Publications

Publications (64)
Preprint
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The reasonability of considering time as a fuzzy concept is demonstrated in ,. One of the major questions which arise here is the new definitions of Complexity Classes. In ,,…, we show why we should consider time a fuzzy concept. It is noticeable to mention that that there were many attempts to consider time as a Fuzzy concept, in P...
Preprint
The approximation of natural numbers subsets has always been one of the fundamental issues in computability theory. Computable approximation, $\Delta_2$-approximation, as well as introducing the generically computable sets have been some efforts for this purpose. In this paper, a type of approximation for natural numbers subsets by computably enume...
Article
Full-text available
In this paper, we generalize the problems of finding simple polygons with minimum area, maximum perimeter, and maximum number of vertices, so that they contain a given set of points and their angles are bounded by α + π where α ( 0 ≤ α ≤ π ) is a parameter. We also consider the maximum angle of each possible simple polygon crossing a given set of p...
Preprint
In this paper, we generalize the problems of finding simple polygons with the minimum area, maximum perimeter and maximum number of vertices so that they contain a given set of points and their angles are bounded by $\alpha+\pi$ where $\alpha$ ($0\leq\alpha\leq \pi$) is a parameter. We also consider the maximum angle of each possible simple polygon...
Preprint
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Let $S$ be a set of points in the plane, $CH$ be the convex hull of $S$, $\wp(S)$ be the set of all simple polygons crossing $S$, $\gamma_P$ be the maximum angle of polygon $P \in \wp(S)$ and $\theta =min_{P\in\wp(S)} \gamma_P$. In this paper, we prove that $\theta\leq 2\pi-\frac{2\pi}{r.m}$ such that $m$ and $r$ are the number of edges and interna...
Article
In practical purposes for some geometrical problems, specially the fields in common with computer science, we deal with information of some finite number of points. The problem often arises here is: “How are we able to define a plausible distance function on a finite three dimensional space?” In this paper, we define such a distance function in ord...
Article
Bounding hulls such as convex hull, α-shape, χ-hull, concave hull, crust, etc. offer a wide variety of useful applications. In this paper, we explore another bounding hull, namely α-concave hull, as a generalization of convex hull. The parameter α determines the smoothness level of the constructed hull on a set of points. We show that it is NP-hard...
Preprint
Full-text available
Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a vers...
Article
R. Hamilton defined Ricci flow as evolution of Riemannian metrics satisfying a weak parabolic partial differential equation. We have considered and studied Ricci flow as an integral curve of a certain vector field in the manifold of Riemannian metrics. In this paper, we study properties of this integral curve and find some results on the stability...
Article
The 1.5D terrain guarding problem examines a 1.5D terrain as an x-monotone polygonal chain in a plane to find the minimum guarding set for a given input terrain. This problem is NP-complete. In real world applications, guard power is limited and can only cover things within a range. Considering this limitation, the present study introduces the “ter...
Article
The vehicle routing problem (VRP) is the problem of designing optimal delivery from a given depot in order to satisfy the customer population demand by a similar fleet of vehicles. It is noted that a considerable part of the drivers' benefits is related to their traveled distance; therefore, the balance of the route based on 'vehicles travelled dis...
Article
Full-text available
In the heterogeneous fixed fleet open vehicle routing problem (HFFOVRP), several different types of vehicles can be used to service the customers. The types of vehicles are different in terms of capacity, fixed cost, and variable cost. In this problem, the vehicles are not required to return to the depot after completing a service and the number of...
Article
The vehicle routing problem VRP is usually studied in two dimensional Euclidean spaces. In this paper a variant of VRP was proposed, when the points are lying in the three dimensional space, as it is often the case in the real problem. The cost matrix of the consumed energy was not symmetric. The minimum cost of total consumed energy was determined...
Article
A 1.5D terrain is a region on a plane determined by an x-monotone polygonal chain. A set G of points on the terrain is called a guarding set if every point on the terrain is seen by some point in G. In the 1.5D terrain guarding problem we are given a 1.5D terrain and the goal is to find the minimum guarding set for the given input terrain. It is pr...
Conference Paper
Vehicle routing problem (VRP) is one of the most important transportation problems in such a way that most of the transportation problems are changeable to it. This problem can be considerably effective in transportation and the costs arising from it. The VRP with some constraints and limitations become closer to the actual world. The generalized p...
Article
Full-text available
Here, by introducing a version of Unexpected hanging paradox first we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system could support it. Finally, we propose a claim in the subject of axiomatizibility. Based on this claim, havi...
Article
Full-text available
Image reconstruction is an important part of computed tomography imaging systems, which converts the measured data into images. Because of high computational cost and slow convergence of iterative reconstruction algorithms, these methods are not widely used in practice. In this paper, we propose a hybrid iterative algorithm by combining multigrid m...
Article
This paper is a further investigation of a project carried out in Didehvar and Ghasemloo (2009) to study effective aspects of the metric logic. We prove an effective version of the omitting types theorem. We also present some concrete computable constructions showing that both the separable atomless probability algebra and the rational Urysohn spac...
Book
This work includes two parts. The first part of the work is about a particular computably enumerable sets (c.e. sets). It includes a novel generalization of an immediate result of Rogers' fixed point Theorem. The second part of this work answers a question raised by B. Poizat. The classical theory of computation was started by the works of Gödel, T...
Article
Full-text available
The open vehicle routing problem (OVRP) is a variant of vehicle routing problem (VRP) in which the vehicles are not required to return to the depot after completing a service. Since this problem belongs to NP-hard Problems, many metaheuristic approaches like ant colony optimization (ACO) have been used to solve it in recent years. The ACO has some...
Article
Full-text available
The vehicle routing problem (VRP) is a well-known NP-Hard problem in operation research which has drawn enormous interest from many researchers during the last decades because of its vital role in planning of distribution systems and logistics. This article presents a modified version of the elite ant system (EAS) algorithm called HEAS for solving...
Article
Full-text available
The vehicle routing problem (VRP) is a well-known NP-Hard problem in operational research which has drawn enormous interest from many researchers during the last decades because of its vital role in planning of distribution systems and logistics. This article presents a modified version of the elite ant system (EAS) algorithm for solving the VRP. T...
Article
One of the most important extensions of the vehicle routing problem is the vehicle routing problem with simultaneous pickup and delivery (VRPSPD) in which the objective is to minimize the distance traveled by using a fleet of vehicles for servicing a set of customers. Because the VRPSPD is an NP-hard problem, practical large-scale instances of this...
Article
Full-text available
A b s t r a c t The iterative reconstruction algorithms are able to reconstruct computed tomography images with higher quality compared with the analytical algorithm when the projection data is noisy or incomplete. The main disadvantages of the iterative algorithms are its high demand on computation and slow convergence. In this paper, our goals ar...
Article
Full-text available
This article presents a new modified version of the ant colony optimization (ACO) mixed with insert, swap and 2-opt algorithm called NMACO for solving the multiple traveling salesman problem (MTSP) which utilizes an effective criterion for escaping from the local optimum points. The MTSP is one of the most important combinatorial optimization probl...
Article
The vehicle routing problem (VRP) is a well-known combinatorial optimisation problem and holds a central place in logistics management. Many exact, heuristic and metaheuristic approaches have been proposed to solve VRP. An important variant of the VRP arises when a fleet of vehicles is fixed and characterised by different capacities for distributio...
Article
Full-text available
Convex hull is a widespread and frequently used concept in computational geometry. In this paper, alpha convex hull is defined as a generalization of convex hull. Here, by proposing an algorithm, it is shown that the construction of alpha convex hull is efficiently computable. Additionally, some applications and methods are presented and the new ma...
Article
Full-text available
In the current paper we have investigated the capacitated distance constraint vehicle routing problem for the standard approximation algorithm. This problem consists of a number of different types of vehicles at the depot which differ at their capacity, cost and maximum distance bound. We have designed an approximation algorithm for this problem in...
Article
Full-text available
One basic requirement of many studies is the necessity of classifying data. Clustering is a proposed method for summarizing networks. Clustering methods can be divided into two categories named model-based approaches and algorithmic approaches. Since the most of clustering methods depend on their input parameters, it is important to evaluate the re...
Conference Paper
Full-text available
The routing cost of a spanning tree in a weighted and connected graph is defined as the total cost of paths between all pairs of vertices. Mini- mum routing cost spanning tree problem is an NP-Hard problem. We present a GRASP with path-relinking metaheuristic algorithm for this problem. GRASP method is a multi-start algorithm that in each iteration...
Working Paper
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Research
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The enumeration of elements of c.e. sets in the theory of computability and computational complexity has already been investigated. However, the order of this enumeration has received less attention. The enumeration orders of elements of c.e. sets by means of Turing machines on natural numbers are investigated. In this paper, we consider the enumer...
Research
Full-text available
The enumeration of elements of c.e. sets in the theory of computability and computational complexity has already been investigated. However, the order of this enumeration has received less attention. The enumeration orders of elements of c.e. sets by means of Turing machines on natural numbers are investigated. In this paper, we consider the enumer...
Conference Paper
Full-text available
Abstract. Supply chain is known as one the most impor tant subject on the economic science. In recent years after 2007, widespre ad researches have been done on supply chain management (SCM), proposed as an independent course and many books published on this subject. Unfortunately, most of the previous researches focused on the study of price e...
Article
Full-text available
In practical purposes for some geometrical problems in computer science we have as information the coordinates of some finite points in surface instead of the whole body of a surface. The problem arised here is: "How to define a distance function in a finite space?" as we will show the appropriate function for this purpose is not a metric function....
Article
Full-text available
Here, by introducing a version of "Unexpected hanging paradox" we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system could support that. In the end, we propose a claim as a question. Based on this claim, having an axiomatic syst...
Article
Full-text available
"How much c.e. sets could cover a given set?" in this paper we are going to answer this question. Also, in this approach some old concepts come into a new arrangement. The major goal of this article is to introduce an appropriate definition for this purpose. Introduction In Computability Theory (Recursion Theory) in the first step we wish to recogn...
Article
Full-text available
This article presents a new algorithm which is a modified version of the elite ant system (EAS) algorithm. The new version utilizes an effective criterion for escaping from the local optimum points. In contrast to the classical EAC algorithms, the proposed algorithm uses only a global updating, which will increase pheromone on the edges of the best...
Article
Full-text available
For a subset K ⊆ [0, 1], the notion of K-satisfiability is a generalization of the usual satisfiability in first order fuzzy logics. A set Γ of closed formulas in a first order language τ is K-satisfiable, if there exists a τ-structure such that ∥ σ ∥ ∈ K, for any σ ∈ Γ. As a consequence, the usual compactness property can be replaced by the K-comp...
Conference Paper
Throughout this article we develop and change the definitions and the ideas in , in order to consider the efficiency of functions and complexity time problems. The central idea here is effective enumeration and listing, and efficiency of function which is defined between two sets proposed in basic definitions. More in detail, it might be tha...
Article
Full-text available
In [arXiv:1006.4939] the enumeration order reducibility is defined on natural numbers. For a c.e. set A, [A] denoted the class of all subsets of natural numbers which are co-order with A. In definition 5 we redefine co-ordering for rational numbers. One of the main questions there, was: "For a specific c.e. set A, consider set of all enumerations o...
Article
Full-text available
This article presents a model which is capable of learning and abstracting new concepts based on comparing observations and finding the resemblance between the observations. In the model, the new observations are compared with the templates which have been derived from the previous experiences. In the first stage, the objects are first represented...
Article
Full-text available
Throughout this article we develop and change the definitions and the ideas in "arXiv:1006.4939", in order to consider the efficiency of functions and complexity time problems. The central idea here is effective enumeration and listing, and efficiency of function which is defined between two sets proposed in basic definitions. More in detail, it mi...
Article
Full-text available
In this paper we have investigated enumeration orders of elements of r.e. sets enumerated by means of Turing machines. We have defined a reducibility based on enumeration orders named "Enumeration Order Reducibility" on computable functions and also r.e. sets and studied their properties. Based on this reducibility we introduce an equivalence relat...
Article
In this paper, we introduce a foundation for computable model theory of rational Pavelka logic (an extension of {\L}ukasiewicz logic) and continuous logic, and prove effective versions of some theorems in model theory. We show how to reduce continuous logic to rational Pavelka logic. We also define notions of computability and decidability of a mod...
Article
Full-text available
In this article we define a new reducibility based on the enumeration orders of r.e. sets. Comment: This paper is the second version of our work on Enumeration Orders
Article
Though numerous approaches have been proposed for face recognition. In this paper we propose a novel face recognition approach based on adaptively weighted patch local statistic in multi dimensional (LMDS) when only one exemplar image per person is available. In this approach, a face image is decomposed into a set of equal-sized patches in a non-ov...
Article
Full-text available
Throughout this article the major idea and conclusion is about comparing this method with some very famous methods like fourier series and wavelet, to show that the power of this approximation method is as much as to predicate many natural and finance methods, something which we can not say the same for wavelets and Fourier series, since this metho...
Article
Full-text available
An independent set in a graph G is a set of vertices no two of which are joined by an edge. A vertex-weighted graph associates a weight with every vertex in the graph. A vertex-weighted graph G is called a unique independence vertex-weighted graph if it has a unique independent set with maximum sum of weights. Although, in this paper we observe tha...
Article
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In this paper we offer a metric similar to graph edit distance which measures the distance between two (possibly infinite)weighted graphs with finite norm (we define the norm of a graph as the sum of absolute values of its edges). The main result is the completeness of the space. Some other analytical properties of this space are also investigated....
Article
Full-text available
Could we define I? Throughout this article we give a negative answer to this question. More exactly, we show that there is no definition for I in a certain way. But this negative answer depends on our definition of definability. Here, we try to consider sufficient generalized definition of definability. In the middle of paper a paradox will arise w...
Article
Could we define I? Throughout this article we give a negative answer to this question. More exactly, we show that there is no definition for I in a certain way. But this negative answer depends on our definition of definability. Here, we try to consider sufficient generalized definition of definability. In the middle of paper a paradox will arise w...
Article
This paper investigates inventory management in a multi channel distribution system consisting of one manufacturer and an arbitrary number of retailers that face stochastic demand. Existence of the pure Nash equilibrium is proved and parameter restriction which implies uniqueness of it is derived. Also the Stackelberg game where the manufacturer pl...
Technical Report
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In this paper, we have compared r.e. sets based on their enumeration orders with Turing machines. Accordingly, we have defined novel concept uniformity for Turing machines and r.e. sets and have studied some relationships between uniformity and both one-reducibility and Turing reducibility. Furthermore, we have defined type-2 uniformity concept and...
Article
The rank aggregation problem is an old problem which arises in many different settings. Let A={1,2,…,n} be the set of alternatives. Suppose δ1,δ2,…,δk are some individual preferences on A. The problem is to find a rank ordering δ such that ∑1⩽i⩽kd(δ,δi) is the minimum among all rank orderings, where d is a metric on the set of the rank orderings on...
Article
We define a class of so-called ∑(n)-sets as a natural closure of recursively enumerable sets Wn under the relation “∈” and study its properties.
Article
One of the highly contraversial discussions in philosophy of mind is equivalence of human being mind and machines. Here we show that no one could prove that, in certain he is a machine
Article
Abstract. There is no doubt that one of the most important problems for recent philosophers is comparison of man and machine abilities. Questions such “Can machines think?”, “Have machines consciousness?”, or this more general question that “Is man a machine?” are questions which answering them has a special importance for contemporary philosophers...