In many multiple criteria optimization problems preserving fairness among individual outcomes becomes an important issue. This is particularly true for systems that are designed for multiple users or services like computer or telecommunication networks. In this paper we investigate a new approach to the resource allocation preserving the, so called, Max-Min Fairness (MMF) in the solution. We an...

the network design problem (ndp) is one of the important problems in combinatorial optimization. among the network design problems, the multicommodity capacitated network design (mcnd) problem has numerous applications in transportation, logistics, telecommunication, and production systems. the mcnd problems with splittable flow variables are np-hard, which means they require exponential time t...

Network flow problems form a core area of Combinatorial Optimization. Their significance arises both from their very large number of applications and their theoretical importance. This thesis focuses on efficient exact algorithms for network flow problems in P and on approximation algorithms for NP -hard variants such as disjoint paths and unsplittable flow. Given an n-vertex, m-edge directed n...

To the best of our knowledge very few methods have been proposed in previous studies for comparing intuitionistic fuzzy (IF) numbers. In this paper, the limitations and the shortcomings of all these existing methods are pointed out. In order to overcome these limitations and shortcomings a new ranking approach—by modifying an existing ranking approach—is proposed for comparing IF numbers. Thus,...

In this paper, we introduce a new framework for approximately solving flow problems in capacitated, undirected graphs and apply it to provide asymptotically faster algorithms for the maximum s-t flow and maximum concurrent multicommodity flow problems. For graphs with n vertices and m edges, it allows us to find an ε-approximate maximum s-t flow in time O(m1+o(1)ε−2), improving on the previous ...

In many application areas engineering, communications, logistics, manufacturing, transportation, different non-homogeneous commodities are distributed over the same underlying network. Usually the separate commodities share common arc capacities that restrict the integrated flow of the gross commodities on the arc. Furthermore, there exists a mutual interaction between the commodities. The ge...

We consider the real-world problem of extending a given infrastructure network in order to connect new customers. By representing the infrastructure by a single root node, this problem can be formulated as a 2-root-connected prize-collecting Steiner network problem in which certain customer nodes require two node-disjoint paths to the root, and other customers only a simple path. Herein, we pre...

We consider the real-world problem of extending a given infrastructure network in order to connect new customers. By representing the infrastructure by a single root node, this problem can be formulated as a 2-root-connected prize-collecting Steiner network problem in which certain customer nodes require two node-disjoint paths to the root, and other customers only a simple path. Herein, we pre...

nowadays, the environmental impact of transportation project and, especially air pollution impacts, are major concerns in evaluating transportation projects. based on this concern, beside definition of traditional objective functions like total travel time and total investment cost, different type of environmental related function is considered as objective function in urban network design. in ...

Let T be an even subset of the vertices of a graph G. A T-cut is an edge-cutset of the graph which divides T into two odd sets. We prove that if G is bipartite, then the maximum number of disjoint !T-cuts is equal to the minimum cardinality of a set of edges which meets every T-cut. (A weaker form of this was proved by Edmonds and Johnson.) We deduce a solution to the real-valued multi-commodit...