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We develop two simple and efficient approximation algorithms for the continuous $k$-medians problems, where we seek to find the optimal location of $k$ facilities among a continuum of client points in a convex polygon $C$ with $n$ vertices…
We survey the main formulations and solution methods for two-dimensional orthogonal cutting and packing problems, where both items and bins are rectangles. We focus on exact methods and relaxations for the four main problems from the…
In this paper, we consider the resource allocation problem in a network with a large number of connections which are used by a huge number of users. The resource allocation problem under discussion is a maximization problem with linear…
Some recent works in machine learning and computer vision involve the solution of a bi-level optimization problem. Here the solution of a parameterized lower-level problem binds variables that appear in the objective of an upper-level…
The p-median problem concerns the location of facilities so that the sum of distances between the demand points and their nearest facility is minimized. We study a variant of this classic location problem where minimum distance constraints…
Packing problems are an important class of optimization problems. The probably most well-known problem if this type is knapsack and many generalizations of it have been studied in the literature like Two-dimensional Geometric Knapsack…
The Maximum Agreement Forest problem has been extensively studied in phylogenetics. Most previous work is on two binary phylogenetic trees. In this paper, we study a generalized version of the problem: the Maximum Agreement Forest problem…
We consider the problem of embedding the Steiner points of a Steiner tree with given topology into the rectilinear plane. Thereby, the length of the path between a distinguished terminal and each other terminal must not exceed given length…
Given a set $P$ of $n$ points in the plane, the $k$-center problem is to find $k$ congruent disks of minimum possible radius such that their union covers all the points in $P$. The $2$-center problem is a special case of the $k$-center…
Given a directed graph $G=(V,A)$, the Directed Maximum Leaf Spanning Tree problem asks to compute a directed spanning tree (i.e., an out-branching) with as many leaves as possible. By designing a Branch-and-Reduced algorithm combined with…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
Assigning tasks to service providers is a frequent procedure across various applications. Often the tasks arrive dynamically while the service providers remain static. Preventing task rejection caused by service provider overload is of…
In data centers, up to dozens of tasks are colocated on a single physical machine. Machines are used more efficiently, but tasks' performance deteriorates, as colocated tasks compete for shared resources. As tasks are heterogeneous, the…
In the current industry, the development of optimized mechanical components able to satisfy the customer requirements evolves quickly. Therefore, companies are asked for efficient solutions to improve their products in terms of stiffness…
In bi-objective integer optimization the optimal result corresponds to a set of non-dominated solutions. We propose a generic bi-objective branch-and-bound algorithm that uses a problem-independent branching rule exploiting available…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
The tree inclusion problem is, given two node-labeled trees $P$ and $T$ (the ``pattern tree'' and the ``target tree''), to locate every minimal subtree in $T$ (if any) that can be obtained by applying a sequence of node insertion operations…
We investigate the problem of scheduling the maintenance of edges in a network, motivated by the goal of minimizing outages in transportation or telecommunication networks. We focus on maintaining connectivity between two nodes over time;…
Let $P$ and $S$ be two disjoint sets of $n$ and $m$ points in the plane, respectively. We consider the problem of computing a Steiner tree whose Steiner vertices belong to $S$, in which each point of $P$ is a leaf, and whose longest edge…
We determine the maximum distance between any two of the center, centroid, and subtree core among trees with a given order. Corresponding results are obtained for trees with given maximum degree and also for trees with given diameter. The…