# Fabio FuriniSapienza University of Rome | la sapienza · Department of Computer, Automatic and Management Engineering "Antonio Ruberti"

Fabio Furini

Doctor of Philosophy

## About

64

Publications

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Introduction

I am an Associate Professor at the Department of Computer, Control and Management Engineering, Sapienza University of Rome. From 2020 to 2021 I have been a Research Fellow at the Italian National Research Council (CNR). From 2013 to 2019, I have been a Maı̂tre de Conférences at the Laboratoire d’analyse
et modélisation de systèmes pour l’aide à la décision (LAMSADE) of Université Paris-Dauphine.
I am a researcher in the fields of mathematical programming and discrete optimization.

Additional affiliations

February 2020 - August 2021

September 2013 - January 2020

September 2012 - August 2013

## Publications

Publications (64)

Given a graph, the maximum clique problem (MCP) asks for determining a complete subgraph with the largest possible number of vertices. We propose a new exact algorithm, called CliSAT, to solve the MCP to proven optimality. This problem is of fundamental importance in graph theory and combinatorial optimization due to its practical relevance for a w...

We investigate the problem of separating cover inequalities of maximum-depth exactly. We propose a pseudopolynomial-time dynamic-programming algorithm for its solution, thanks to which we show that this problem is weakly $${\mathcal {N}}{\mathcal {P}}$$ N P -hard (similarly to the problem of separating cover inequalities of maximum violation). We c...

The aim of this letter is to design and computationally test several improvements for the compact integer linear programming (ILP) formulations of the temporal bin packing problem with fire-ups (TBPP-FU). This problem is a challenging generalization of the classical bin packing problem in which the items, interpreted as jobs of given weight, are ac...

Exploiting Bilevel Optimization Techniques to Disconnect Graphs into Small Components
In order to limit the spread of possible viral attacks in a communication or social network, it is necessary to identify critical nodes, the protection of which disconnects the remaining unprotected graph into a bounded number of shores (subsets of vertices) of li...

In this article we address the problem of finding lower bounds for small Ramsey numbers R(m, n) using circulant graphs. Our constructive approach is based on finding feasible colorings of circulant graphs using Integer Programming (IP) techniques. First we show how to model the problem as a Stackelberg game and, using the tools of bilevel optimizat...

A binary constraint satisfaction problem (BCSP) consists in determining an assignment of values to variables that is compatible with a set of constraints. The problem is called binary because the constraints involve only pairs of variables. The BCSP is a cornerstone problem in Constraint Programming (CP), appearing in a very wide range of real-worl...

Given a graph G and an interdiction budget k∈N, the Edge Interdiction Clique Problem (EICP) asks to find a subset of at most k edges to remove from G so that the size of the maximum clique, in the interdicted graph, is minimized. The EICP belongs to the family of interdiction problems with the aim of reducing the clique number of the graph. The EIC...

A binary constraint satisfaction problem (BCSP) consist in determining an assignment of values to variables which is compatible with a set of constraints. The problem is called binary because the constraints involve only pairs of variables. The BCSP is a cornerstone problem in Constraint Programming (CP), appearing in a very wide range of real-worl...

We study the family of problems of partitioning and covering a graph into/with a minimum number of relaxed cliques. Relaxed cliques are subsets of vertices of a graph for which a clique-defining property—for example, the degree of the vertices, the distance between the vertices, the density of the edges, or the connectivity between the vertices—is...

A proper coloring of a given graph is an assignment of a positive integer number (color) to each vertex such that two adjacent vertices receive different colors. This paper studies the Minimum Sum Coloring Problem (MSCP), which asks for finding a proper coloring while minimizing the sum of the colors assigned to the vertices. We propose the first b...

Given a graph G and an interdiction budget k ∈ N, the Edge Interdiction Clique Problem (EICP) asks to find a subset of at most k edges to remove from G so that the size of the maximum clique, in the interdicted graph, is minimized. The EICP belongs to the family of interdiction problems with the aim of reducing the clique number of the graph. The E...

We study the Knapsack Problem with Conflicts, a generalization of the Knapsack Problem in which a set of conflicts specifies pairs of items which cannot be simultaneously selected. In this work, we propose a novel combinatorial branch-and-bound algorithm for this problem based on an n-ary branching scheme. Our algorithm effectively combines differe...

Divide and conquer, from Latin divide et impera, is one of the key techniques for tackling combinatorial optimization problems. It relies on the idea of decomposing complex problems into a sequence of subproblems that are then easier to handle. Decomposition techniques (such as Dantzig-Wolfe, Lagrangian, or Benders decomposition) are extremely effe...

We propose an exact lexicographic dynamic programming pricing algorithm for solving the Fractional Bin Packing Problem with column generation. The new algorithm is designed for generating maximal columns of minimum reduced cost which maximize, lexicographically, one of the measures of maximality we investigate. Extensive computational experiments r...

We study the maximum edge-weighted clique problem, a problem related to the maximum (vertex-weighted) clique problem which asks for finding a complete subgraph (i.e., a clique) of maximum total weight on its edges.
The problem appears in a wide range of applications, including bioinformatics, material science, computer vision, robotics, and many mo...

We study an extension of the classical Bin Packing Problem, where each item consumes the bin capacity during a given time window that depends on the item itself. The problem asks for finding the minimum number of bins to pack all the items while respecting the bin capacity at any time instant. A polynomial-size formulation, an exponential-size form...

We extend the definition of sandwich line-graphs, a class of auxiliary graphs the stable sets ofwhich are in 1-to-1 correspondence with the colorings of the original graph, from graphs to parti-tioned graphs. This way, we obtain a one-to-one correspondence between stable sets and partitioncolorings.
(6) (PDF) A note on Selective line-graphs and p...

We perform a theoretical and computational study of the classical linearisation techniques (LT) and we propose a new LT for binary quadratic problems (BQPs). We discuss the relations between the linear programming (LP) relaxations of the considered LT for generic BQPs. We prove that for a specific class of BQP all the LTs have the same LP relaxatio...

The family of critical node detection problems asks for finding a subset of vertices, deletion of which minimizes or maximizes a predefined connectivity measure on the remaining network. We study a problem of this family called the k-vertex cut problem. The problem asks for determining the minimum weight subset of nodes whose removal disconnects a...

We study the Maximum Weighted Clique Problem (MWCP), a generalization of the Maximum
Clique Problem in which weights are associated with the vertices of a graph. The MWCP calls
for determining a complete subgraph of maximum weight. We design a new combinatorial
branch-and-bound algorithm for the MWCP, which relies on an effective bounding procedure...

We study the two player zero-sum Stackelberg game in which the leader interdicts (removes) a limited number of vertices from the graph, and the follower searches for the maximum clique in the interdicted graph. The goal of the leader is to derive an interdiction policy which will result in the worst possible outcome for the follower. This problem h...

We study an extension of the classical Bin Packing Problem, where each item consumes the bin capacity during a given time window that depends on the item itself. The problem asks for finding the minimum number of bins to pack all the items while respecting the bin capacity at any time instant. A polynomial-size formulation, an exponential-size form...

Covering problems constitute a fundamental family of facility location problems. This paper introduces a new exact algorithm for two important members of this family: (i) the maximal covering location problem (MCLP), which requires finding a subset of facilities that maximizes the amount of customer demand covered while respecting a budget constrai...

This paper describes a new instance library for quadratic programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function and/or the constraints are quadratic. QP is a very diverse class of problems, comprising sub-classes ranging from trivial to undecidable. This diversity is reflected in the...

Given an undirected graph G=(V,E), a vertex k-cut of G is a vertex subset of V the removing of which disconnects the graph in at least k components. Given a graph G and an integer k≥2, the vertex k-cut problem consists in finding a vertex k-cut of G of minimum cardinality. We first prove that the problem is NP-hard for any fixed k≥3. We then presen...

In spite of being an extremely successful method to tackle mathematical programs involving a very large number of variables, Column Generation (CG) is known to suffer from stabilization issues which can slow down its convergence significantly. In this article, we propose a new parameter-free stabilization technique for CG based on solving a lexicog...

Given a set of items, each characterized by a profit and a weight, we study the problem of maximizing the product of the profits of the selected items, while respecting a given capacity. To the best of our knowledge this is the first manuscript that studies this variant of the knapsack problem which we call Product Knapsack Problem (PKP). We show t...

We study an extension of the Bin Packing Problem, where items consume the bin capacity during a time window only. The problem asks for finding the minimum number of bins to pack all the items respecting the bin capacity at any instant of time. Both a polynomial-size formulation and an extensive formulation are studied. Moreover, various heuristic a...

This paper addresses the problem of optimal planning of a liner service for a barge container shipping company. Given estimated weekly demands between pairs of ports, our goal is to determine the subset of ports to be called and the amount of containers to be shipped between each pair of ports, so as to maximize the profit of the shipping company....

We study the Partition Coloring Problem (PCP), a generalization of the Vertex Coloring Problem where the vertex set is partitioned. The PCP asks to select one vertex for each subset of the partition in such a way that the chromatic number of the induced graph is minimum. We propose a new Integer Linear Programming formulation with an exponential nu...

We consider a generalization of the knapsack problem in which items are partitioned into classes, each characterized by a fixed cost and capacity. We study three alternative Integer Linear Programming formulations. For each formulation, we design an efficient algorithm to compute the linear programming relaxation (one of which is based on Column Ge...

We propose an improvement of the Approximated Projected Perspective Reformulation (AP²R) for dealing with constraints linking the binary variables. The new approach solves the Perspective Reformulation (PR) once, and then use the corresponding dual information to reformulate the problem prior to applying AP²R, thereby combining the root bound quali...

Given a set of items with profits and weights and a knapsack capacity, we study the problem of finding a maximal knapsack packing that minimizes the profit of the selected items. We propose an effective dynamic programming (DP) algorithm which has a pseudo-polynomial time complexity. We demonstrate the equivalence between this problem and the probl...

Given an undirected graph, the Vertex Coloring Problem (VCP) consists of assigning a color to each vertex of the graph in such a way that two adjacent vertices do not share the same color and the total number of colors is minimized. DSATUR-based Branch-and-Bound algorithm (DSATUR) is an effective exact algorithm for the VCP. One of its main drawbac...

Given a set of n items with profits and weights and a knapsack capacity C, we study the problem of finding a maximal knapsack packing that minimizes the profit of selected items. We propose for the first time an effective dynamic programming (DP) algorithm which has O(nC) time complexity and O(n + C) space complexity. We demonstrate the equivalence...

In Vertex Coloring Problems, one is required to assign a color to each vertex of an undirected graph in such a way that adjacent vertices receive different colors, and the objective is to minimize the cost of the used colors. In this work we solve four different coloring problems formulated as Maximum Weight Stable Set Problems on an associated gra...

The integration of drones into civil airspace is one of the most challenging problems for the automation of the controlled airspace, and the optimization of the drone route is a key step for this process. In this paper, we optimize the route planning of a drone mission that consists of departing from an airport, flying over a set of mission way poi...

A rich lot-sizing problem is studied in this manuscript which comes from a real-world application. Our new lot-sizing problem combines several features, i.e., parallel machines, production time windows, backlogging, lost sale and setup carryover. Three mixed integer programming formulations are proposed. We theoretically and computationally compare...

The Temporal Knapsack Problem (TKP) is a generalization of the standard Knapsack Problem where a time horizon is considered, and each item consumes the knapsack capacity during a limited time interval only. In this paper we solve the TKP using what we call a Recursive Dantzig-Wolfe Reformulation (DWR) method. The generic idea of Recursive DWR is to...

We propose a framework to model general guillotine restrictions in two-dimensional cutting problems formulated as mixed-integer linear programs (MIPs). The modeling framework requires a pseudopolynomial number of variables and constraints, which can be effectively enumerated for medium-size instances. Our modeling of general guillotine cuts is the...

The perspective reformulation (PR) of a Mixed-Integer NonLinear Program with semi-continuous variables is obtained by replacing each term in the (separable) objective function with its convex envelope. Solving the corresponding continuous relaxation requires appropriate techniques. Under some rather restrictive assumptions, the Projected PR ((Formu...

Lazy reformulations of classical combinatorial optimization problems are new and challenging classes of problems. In this paper we focus on the Lazy Bureaucrat Problem (LBP) which is the lazy counterpart of the knapsack problem. Given a set of tasks with a common arrival time and deadline, the goal of a lazy bureaucrat is to schedule a least profit...

We consider the Train Timetabling Problem (TTP) in a railway node (i.e. a set of stations in an urban area interconnected by tracks), which calls for determining the best schedule for a given set of trains during a given time horizon, while satisfying several track operational constraints. In particular, we consider the context of a highly congeste...

We consider a generalization of the 0-1 knapsack problem in which the profit of each item can take any value in a range characterized by a minimum and a maximum possible profit. A set of specific profits is called a scenario. Each feasible solution associated with a scenario has a regret, given by the difference between the optimal solution value f...

In a scenario characterized by a continuous growth of air transportation demand, the runways of large airports serve hundreds of aircraft every day. Aircraft sequencing is a challenging problem that aims to increase runway capacity in order to reduce delays as well as the workload of air traffic controllers. In many cases, the air traffic controlle...

Given an indirected graph G = (V;E), a Vertex k-Separator is a subset of the vertex set V such that, when the separator is removed from the graph, the remaining vertices can be partitioned into k subsets that are pairwise edge-disconnected. In this paper we focus on the Balanced Vertex k-Separator Problem, i.e., the problem of finding a minimum car...

Dantzig-Wolfe decomposition (or reformulation) is well-known to pro-vide strong dual bounds for specially structured mixed integer programs (MIPs) in practice. However, the method is not implemented in any state-of-the-art MIP solver as it is considered to require structural problem knowledge and tailoring to this structure. We provide a computatio...

In this paper we present state space reduction techniques for a dynamic programming algorithm applied to the Aircraft Sequencing Problem (ASP) with Constrained Position Shifting (CPS). We consider the classical version of the ASP, which calls for determining the order in which a given set of aircraft should be assigned to a runway at an airport, su...

A Look-Up-Table-based method is proposed to generate random instances of an antipodal n-dimensional vector so that its 2-nd order statistics are as close as possible to a given specification. The method is based on linear optimization and exploits column-generation techniques to cope with the exponential complexity of the task. It yields a LUT whos...

We consider a Two-Dimensional Cutting Stock Problem (2DCSP) where stock of different sizes is available, and a set of rectangular items has to be obtained through two-stage guillotine cuts. We propose and computationally compare three Mixed-Integer Programming models for the 2DCSP developing formulations from the literature. The first two models ha...

We study a natural generalization of the knapsack problem, in which each item exists only for a given time interval. One has to select a subset of the items as in the classical case, guaranteeing that for each time instant, the set of existing selected items has total weight no larger than the knapsack capacity. We focus on the exact solution of th...

The principal idea of this paper is to exploit Semidefinite Programming (SDP) relaxation within the framework provided by Mixed Integer Nonlinear Programming (MINLP) solvers when tackling Binary Quadratic Problems. We included the SDP relaxation in a state-of-the-art MINLP solver as an additional bounding technique and demonstrated that this idea c...

We consider a conflict-free scheduling problem which arises in railway networks, where ideal timetables have been provided for a set of trains, but where these timetables may be conflicting. We use a space-time graph approach from the railway scheduling literature in order to develop a fast heuristic which resolves conflicts by adjusting the ideal...

We consider the Weighted Vertex Coloring Problem (WVCP), in which a positive weight is associated to each vertex of a graph. In WVCP, one is required to assign a color to each vertex in such a way that colors on adjacent vertices are different, and the objective is to minimize the sum of the costs of the colors used, where the cost of each color is...

Aircraft sequencing on the runway is a challenging optimization problem that aims to reduce the delays and the air traffic controllers workload in a scenario characterized by a continuous growth of the air transportation demand. In this paper we consider the problem of sequencing both arrivals and departures on a single runway airport. We formalize...

We consider a two-dimensional cutting stock problem where stock of different sizes is available, and a set of rectangular items has to be obtained through two-staged guillotine cuts. We propose a heuristic algorithm, based on column generation, which requires as subproblem the solution of a two-dimensional knapsack problem with two-staged guillotin...

Dantzig-Wolfe decomposition is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs) in practice. However, the method is not implemented in any state-of-the-art MIP solver: it needs tailoring to the particular problem; the decomposition must be determined from the typical bordered block-diagonal matrix stru...

## Questions

Questions (2)

Does anybody know the complexity of this problem? Many thanks

I'm interested in the separation of the odd set inequalities for the matching polytope. Thank you for your help!!!

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