Cologne Twente Workshop on Graphs and Combinatorical Optimization, 2008
During the last two decades, there has been a growing interest in locating extensive facil- ities... more During the last two decades, there has been a growing interest in locating extensive facil- ities, such as paths, on networks. In this paper we study the median path problem without restrictions on its length on the class of connected outerplanar graphs with equal weights assigned to the edges and nonnegative weights associated to the vertices. We provide a O(kn)
Several portfolio selection models take into account practical limitations on the number of asset... more Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACVaR) models, where the assets are limited with the introduction of
Index tracking aims at determining an optimal portfolio that replicates the performance of an ind... more Index tracking aims at determining an optimal portfolio that replicates the performance of an index or benchmark by investing in a smaller number of constituents or assets. The tracking portfolio should be cheap to maintain and update, i.e., invest in a smaller number of constituents than the index, have low turnover and low transaction costs, and should avoid large positions
Automated political districting shares with electronic voting the aim of preventing electoral man... more Automated political districting shares with electronic voting the aim of preventing electoral manipulation and pursuing an impartial electoral mechanism. Political districting can be modelled as multiobjective partitioning of a graph into connected components, where population equality and compactness must hold if a majority voting rule is adopted. This leads to the formulation of combinatorial optimization problems that are extremely hard
In a network, the distsum of a path is the sum of the distances of all vertices to the path, and ... more In a network, the distsum of a path is the sum of the distances of all vertices to the path, and the eccentricity is the maximum distance of any vertex to the path. The Cent-dian problem is the constrained optimization problem which seeks to locate on a network a path which has ...
In this paper we study the Forest Wrapping Problem (FWP) which can be stated as follows: given a ... more In this paper we study the Forest Wrapping Problem (FWP) which can be stated as follows: given a connected graph G = (V,E), with ∣V ∣ = n, let π0 be a partition of G into K (not necessarily connected) components, find a connected partition π* of G that wraps π0 and has maximum number of components. The Forest Wrapping problem is NP-complete on grid graphs while is solvable in O(n log n) time on ladder graphs. We provide a two-phase O(n 2 ) time algorithm for solving FWP on outerplanar graphs.
Page 1. Efficient Algorithms for Finding the (k, l)-Core of Tree Networks Ronald I. Becker Univer... more Page 1. Efficient Algorithms for Finding the (k, l)-Core of Tree Networks Ronald I. Becker University of Cape Town, Rondebosh 7700, South Africa and Department of Mathematics and Technion, Haifa, Israel Isabella Lari and ...
The location of path-shaped facilities on trees has been receiving a growing attention in the spe... more The location of path-shaped facilities on trees has been receiving a growing attention in the specialized literature in the recent years. Examples of such facilities include railroad lines, highways and public transit lines. Most of the papers deal with the problem of locating a path on a tree by minimizing either the maximum distance from the vertices of the tree to the facility or of minimizing the sum of the distances from all the vertices of the tree to the path. However, neither of the two above criteria alone capture all essential elements of a location problem. The sum of the distances criterion alone may result in solutions which are unacceptable from the point of view of the service level for the clients who are located far away from the facilities. On the other hand, the criterion of the minimization of the maximum distance, if used alone, may lead to very costly service systems. In the literature, there is just one paper that considers the problem of finding an optimal location of a path on a tree using combinations of the two above criteria, and efficient algorithms are provided. In particular, the cases where one criterion is optimized subject to a restriction on the value of the other are considered and linear time algorithms are presented. However, these problems do not consider any bound on the length or cost of the facility. In this paper we consider the two following problems: find a path which minimizes the sum of the distances such that the maximum distance from the vertices of the tree to the path is bounded by a fixed constant and such that the length of the path is not greater than a fixed value; find a path which minimizes the maximum distance with the sum of the distances being not greater than a fixed value and with bounded length. From an application point of view the constraint on the length of the path may refer to a budget constraint for establishing the facility. The restriction on the length of the path complicates the two problems but for both of them we give O(nlog2n) divide-and-conquer algorithms.
... a Università di Roma La Sapienza, Dip. Statistica, Probabilità e Statistiche Applicate, P.l... more ... a Università di Roma La Sapienza, Dip. Statistica, Probabilità e Statistiche Applicate, P.le Aldo Moro 5, 00185 Roma, Italy. Received 15 December 2005; accepted 1 July 2007. ... We note here that the graph used in [22] for the reduction, is, in fact, a cactus graph. ...
ABSTRACT In this paper we study a location problem on networks that combines three important issu... more ABSTRACT In this paper we study a location problem on networks that combines three important issues: (1) it considers that facilities are extensive, (2) it handles simultaneously the location of more than one facility, and (3) it incorporates reliability aspects related to the fact that facilities may fail. The problem consists of locating two path-shaped facilities minimizing the expected service cost in the long run, assuming that paths may become unavailable and their failure probabilities are known in advance. We discuss several aspects of the computational complexity of problems of locating two or more reliable paths on graphs, showing that multifacility path location–with and without reliability issues–is a difficult problem even for 2 facilities and on very special classes of graphs. In view of this, we focus on trees and provide a polynomial time algorithm that solves the 2 unreliable path location problem on tree networks in O(n2)O(n2) time, where nn is the number of vertices.
ABSTRACT In this paper, we study the problem of locating path-shaped facilities on a tree network... more ABSTRACT In this paper, we study the problem of locating path-shaped facilities on a tree network with non negative weights associated to the vertices and positive lengths associated to the edges. Our objective is to ensure low variability of the distribution of the distances from the demand points (clients) to a facility. In the location process, we take into account both the maximum and the minimum weighted distances of a client to a facility and we formulate our problem in order to minimize the “Range” function which is defined as the difference between the maximum and the minimum weighted distances from the vertices of the network to a facility. We discuss different formulations of the problem providing polynomial time algorithms for each of them. We solve in polynomial time all the above problems also when an additional constraint on the maximum length of the path is introduced.
Cologne Twente Workshop on Graphs and Combinatorical Optimization, 2008
During the last two decades, there has been a growing interest in locating extensive facil- ities... more During the last two decades, there has been a growing interest in locating extensive facil- ities, such as paths, on networks. In this paper we study the median path problem without restrictions on its length on the class of connected outerplanar graphs with equal weights assigned to the edges and nonnegative weights associated to the vertices. We provide a O(kn)
Several portfolio selection models take into account practical limitations on the number of asset... more Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACVaR) models, where the assets are limited with the introduction of
Index tracking aims at determining an optimal portfolio that replicates the performance of an ind... more Index tracking aims at determining an optimal portfolio that replicates the performance of an index or benchmark by investing in a smaller number of constituents or assets. The tracking portfolio should be cheap to maintain and update, i.e., invest in a smaller number of constituents than the index, have low turnover and low transaction costs, and should avoid large positions
Automated political districting shares with electronic voting the aim of preventing electoral man... more Automated political districting shares with electronic voting the aim of preventing electoral manipulation and pursuing an impartial electoral mechanism. Political districting can be modelled as multiobjective partitioning of a graph into connected components, where population equality and compactness must hold if a majority voting rule is adopted. This leads to the formulation of combinatorial optimization problems that are extremely hard
In a network, the distsum of a path is the sum of the distances of all vertices to the path, and ... more In a network, the distsum of a path is the sum of the distances of all vertices to the path, and the eccentricity is the maximum distance of any vertex to the path. The Cent-dian problem is the constrained optimization problem which seeks to locate on a network a path which has ...
In this paper we study the Forest Wrapping Problem (FWP) which can be stated as follows: given a ... more In this paper we study the Forest Wrapping Problem (FWP) which can be stated as follows: given a connected graph G = (V,E), with ∣V ∣ = n, let π0 be a partition of G into K (not necessarily connected) components, find a connected partition π* of G that wraps π0 and has maximum number of components. The Forest Wrapping problem is NP-complete on grid graphs while is solvable in O(n log n) time on ladder graphs. We provide a two-phase O(n 2 ) time algorithm for solving FWP on outerplanar graphs.
Page 1. Efficient Algorithms for Finding the (k, l)-Core of Tree Networks Ronald I. Becker Univer... more Page 1. Efficient Algorithms for Finding the (k, l)-Core of Tree Networks Ronald I. Becker University of Cape Town, Rondebosh 7700, South Africa and Department of Mathematics and Technion, Haifa, Israel Isabella Lari and ...
The location of path-shaped facilities on trees has been receiving a growing attention in the spe... more The location of path-shaped facilities on trees has been receiving a growing attention in the specialized literature in the recent years. Examples of such facilities include railroad lines, highways and public transit lines. Most of the papers deal with the problem of locating a path on a tree by minimizing either the maximum distance from the vertices of the tree to the facility or of minimizing the sum of the distances from all the vertices of the tree to the path. However, neither of the two above criteria alone capture all essential elements of a location problem. The sum of the distances criterion alone may result in solutions which are unacceptable from the point of view of the service level for the clients who are located far away from the facilities. On the other hand, the criterion of the minimization of the maximum distance, if used alone, may lead to very costly service systems. In the literature, there is just one paper that considers the problem of finding an optimal location of a path on a tree using combinations of the two above criteria, and efficient algorithms are provided. In particular, the cases where one criterion is optimized subject to a restriction on the value of the other are considered and linear time algorithms are presented. However, these problems do not consider any bound on the length or cost of the facility. In this paper we consider the two following problems: find a path which minimizes the sum of the distances such that the maximum distance from the vertices of the tree to the path is bounded by a fixed constant and such that the length of the path is not greater than a fixed value; find a path which minimizes the maximum distance with the sum of the distances being not greater than a fixed value and with bounded length. From an application point of view the constraint on the length of the path may refer to a budget constraint for establishing the facility. The restriction on the length of the path complicates the two problems but for both of them we give O(nlog2n) divide-and-conquer algorithms.
... a Università di Roma La Sapienza, Dip. Statistica, Probabilità e Statistiche Applicate, P.l... more ... a Università di Roma La Sapienza, Dip. Statistica, Probabilità e Statistiche Applicate, P.le Aldo Moro 5, 00185 Roma, Italy. Received 15 December 2005; accepted 1 July 2007. ... We note here that the graph used in [22] for the reduction, is, in fact, a cactus graph. ...
ABSTRACT In this paper we study a location problem on networks that combines three important issu... more ABSTRACT In this paper we study a location problem on networks that combines three important issues: (1) it considers that facilities are extensive, (2) it handles simultaneously the location of more than one facility, and (3) it incorporates reliability aspects related to the fact that facilities may fail. The problem consists of locating two path-shaped facilities minimizing the expected service cost in the long run, assuming that paths may become unavailable and their failure probabilities are known in advance. We discuss several aspects of the computational complexity of problems of locating two or more reliable paths on graphs, showing that multifacility path location–with and without reliability issues–is a difficult problem even for 2 facilities and on very special classes of graphs. In view of this, we focus on trees and provide a polynomial time algorithm that solves the 2 unreliable path location problem on tree networks in O(n2)O(n2) time, where nn is the number of vertices.
ABSTRACT In this paper, we study the problem of locating path-shaped facilities on a tree network... more ABSTRACT In this paper, we study the problem of locating path-shaped facilities on a tree network with non negative weights associated to the vertices and positive lengths associated to the edges. Our objective is to ensure low variability of the distribution of the distances from the demand points (clients) to a facility. In the location process, we take into account both the maximum and the minimum weighted distances of a client to a facility and we formulate our problem in order to minimize the “Range” function which is defined as the difference between the maximum and the minimum weighted distances from the vertices of the network to a facility. We discuss different formulations of the problem providing polynomial time algorithms for each of them. We solve in polynomial time all the above problems also when an additional constraint on the maximum length of the path is introduced.
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Papers by Andrea Scozzari