Sharif Digital Repository

The path-matching problem is to find a set of vertex- or edge-disjoint paths with length constraints in a given graph with a given set of endpoints. This problem has several applications in broadcasting and multicasting in computer networks. In this paper, we study the algorithmic complexity of different cases of this problem. In each case, we either provide a polynomial-time algorithm or prove that the problem is NP-complete. © 2002 Wiley Periodicals, Inc  

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  

Motivated by the bus escape routing problem in printed circuit boards, we study the following rectangle escape problem: given a set S of n axis-aligned rectangles inside an axis-aligned rectangular region R, extend each rectangle in S toward one of the four borders of R so that the maximum density over the region R is minimized. The density of each point p∈R is defined as the number of extended rectangles containing p. We show that the problem is hard to approximate to within a factor better than 3/2 in general. When the optimal density is sufficiently large, we provide a randomized algorithm that achieves an approximation factor of 1+ε with high probability improving over the current best... 

A proper orientation of a graph G=(V,E) is an orientation D of E(G) such that for every two adjacent vertices v and u, dD -(v) ≠ dD -(u) where dD -(v) is the number of edges with head v in D. The proper orientation number of G is defined as χ→(G)=minD∈Γmaxv∈V(G)d D -(v) where Γ is the set of proper orientations of G. We have χ(G)-1≤χ→(G)≤Δ(G), where χ(G) and Δ(G) denote the chromatic number and the maximum degree of G, respectively. We show that, it is NP-complete to decide whether χ→(G)=2, for a given planar graph G. Also, we prove that there is a polynomial time algorithm for determining the proper orientation number of 3-regular graphs. In sharp contrast, we will prove that this problem... 

Removal or suppression of key proteins in an essential pathway of a pathogen is expected to disrupt the pathway and prohibit the pathogen from performing a vital function. Thus disconnecting multiple essential pathways should disrupt the survival of a pathogen even when it has multiple pathways to drug resistance. We consider a scenario where the drug-resistance pathways are unknown. To disrupt these pathways, we consider a cut set S of G, where G is a connected simple graph representing the protein interaction network of the pathogen, so that G-S splits to two partitions such that the endpoints of each pathway are in different partitions. If the difference between the sizes of the two... 

A proper labeling of a graph is an assignment of integers to some elements of a graph, which may be the vertices, the edges, or both of them, such that we obtain a proper vertex coloring via the labeling subject to some conditions. The problem of proper labeling offers many variants and received a great interest during recent years. We consider the algorithmic complexity of some variants of the proper labeling problems, we present some polynomial time algorithms and NP-completeness results for them  

Many genetic algorithms (GA) have been applied to solve different NP-complete combinatorial optimization problems so far. The striking point of using GA refers to selecting a combination of appropriate patterns in crossover, mutation, and and so forth and fine tuning of some parameters such as crossover probability, mutation probability, and and so forth. One way to design a robust GA is to select an optimal pattern and then to search for its parameter values using a tuning procedure. This paper addresses a methodology to both optimal pattern selection and the tuning phases by taking advantage of design of experiments and response surface methodology. To show the performances of the proposed... 

This research deals with a flexible flowshop scheduling problem with the arrival and delivery of jobs in groups and processing them individually. Each group of jobs has a specific release time. Due to the special characteristics of each job, only a specific group of machines in each stage are eligible to process that job. All jobs in a group should be delivered at the same time after processing. The objectives of the problem are the minimization of the sum of the completion time of groups on one hand and the minimization of sum of the differences between the completion time of jobs and the delivery time of the group containing that job (waiting period) on the other hand. The problem can be... 

The efficient scheduling of the independent and sequential tasks on distributed and heterogeneous computing resources within grid computing environments is an NP-complete problem. Therefore, using heuristic approaches to solve the scheduling problem is a very common and also acceptable method in these environments. In this paper, a new task scheduling algorithm based on bee colony optimization approach is proposed. The algorithm uses artificial bees to appropriately schedule the submitted tasks to the grid resources. Applying the proposed algorithm to the grid computing environments, the maximum delay and finish times of the tasks are reduced. Furthermore, the total makespan of the... 

Clustering is the problem of finding relations in a data set in an supervised manner. These relations can be extracted using the density of a data set, where density of a data point is defined as the number of data points around it. To find the number of data points around another point, region queries are adopted. Region queries are the most expensive construct in density based algorithm, so it should be optimized to enhance the performance of density based clustering algorithms specially on large data sets. Finding the optimum set of region queries to cover all the data points has been proven to be NP-complete. This optimum set is called the skeletal points of a data set. In this paper, we... 

A new meta-heuristic algorithm is proposed for constructing multicast trees in real-time multimedia applications such that satisfies two important Quality of Service (QoS) constraints. The QoS based multicast routing problem is a known NP-complete problem that depends on (1) bounded end-to-end delay and link bandwidth along the paths from the source to each destination, and (2) minimum cost of the multicast tree. We evaluate the performance and efficiency of the proposed method with a modified version of the BSMA algorithm which is the best known deterministic heuristic algorithm to delay-constrained multicast problem. Simulation results reveal that the proposed algorithm can achieve a... 

The advent of various real-time multimedia applications in high-speed networks creates a need for quality of service (QoS) based multicast routing. Two important QoS constraints are the bandwidth constraint and the end-to-end delay constraint. The QoS based multicast routing problem is a known NP-complete problem that depends on (1) bounded end-to-end delay and link bandwidth along the paths from the source to each destination, and (2) minimum cost of the multicast tree. In this paper we describe a new representation, called node parent index (NPI) representation, for representing trees and describe harmony operations accord to this representation. The presented algorithm is based on the... 

The critical issue in designing correlated data networks like Wireless Sensor Networks is to minimize the total cost of data transmission in the network, and decrease the amount of data flow. The problem of finding optimal aggregation tree for correlated data gathering in single sink network is considered as an NP-Complete problem and hence heuristic methods are usually applied to solve it[1]. In this paper, we apply genetic algorithm (GA) to solve the problem. In our method, we improve the performance of genetic search by selecting proper initial population. This initial population is determined in two ways, by using Prime's algorithm, and shortest path tree. The main issue is to regard... 

Today's software systems are more frequently composed from preexisting commercial or non-commercial components and connectors. These components provide complex and independent functionality and are engaged in complex interactions. Component-Based Software Engineering (CBSE) is concerned with composing, selecting and designing such components. As the popularity of this approach and hence number of commercially available software components grows, selecting a set of components to satisfy a set of requirements while minimizing cost is becoming more difficult. This problem necessitates the design of efficient algorithms to automate component selection for software developing organizations. We...