In this paper, we study the problem Min-Max 2-Cluster Editing which asks for a modification of a given graph into two maximal cliques by inserting or deleting edges such that the maximum number k of the editing edges incident to any vertex is minimized. We show the NP-hardness of the problem and present a polynomial-time algorithm when k < n/4, in which n is number of vertices. In addition, we ...

In this paper we consider the Frequency Assignment Problem, where the objective is to minimize the cost due to interference arising in a solution. We use a quadratic 0-1 integer programming formulation of the problem as a basis to derive new lower bounds and problem reduction rules. A tree search algorithm, that uses the lower bounds and dominance criteria is also presented. Computational resul...

The Max-Min allocation problem is to distribute indivisible goods to people so as to maximize the minimum utility of the people. We show a (2k − 1)-approximation algorithm for Max-Min when there are k people with subadditive utility functions. We also give a k/α-approximation algorithm (for α ≤ k/2) if the utility functions are additive and the utility of an item for a person is restricted to 0...

Once known to be used exclusively in military domain, unmanned aerial vehicles (drones) have stepped up to become a part of new logistic method in commercial sector called "last-mile delivery". In this novel approach, small unmanned aerial vehicles (UAV), also known as drones, are deployed alongside with trucks to deliver goods to customers in order to improve the service quality or reduce the ...

In the single source unsplittable min-cost flow problem, commodities must be routed simultaneously from a common source vertex to certain destination vertices in a given graph with edge capacities and costs; the demand of each commodity must be routed along a single path so that the total flow through any edge is at most its capacity. Moreover, the total cost must not exceed a given budget. Thi...

The end-to-end assignment of bandwidth to node-pairs (demands) in a communication network can be considered fair if it is distributed according to the max-min fair (MMF) principle. This paper investigates the problem of obtaining an MMF allocation if each demand is required to use exactly one path (i.e., to use unsplittable flows). First it is shown that the problem is NP-hard, both if each dem...

We introduce and study the online house numbering problem, where houses are added arbitrarily along a road and must be assigned labels to maintain their ordering along the road. The online house numbering problem is related to classic online list labeling problems, except that the optimization goal here is to minimize the maximum number of times that any house is relabeled. We provide several a...

To minimize the length of travelling distance of the longest sub-route in vehicle routing problem, the max-min ant system with parameter adaptation is adopted, which can be applied to different datasets in practice. Routes are constructed by sequential and parallel methods for the customers with clustering and random distribution respectively. Since the behavior of ant colony algorithm depends ...

In this paper, we consider two types of problems that have some similarity in their structure, namely, min-min and min-max saddle-point problems. Our approach is based on considering the outer minimization problem as a with inexact oracle. This oracle calculated via solution inner problem, which either or maximization problem. main assumptions are smooth available mixed: it only possible to eva...