Alessandro Maddaloni

Sufficient Conditions for a Digraph to be Supereulerian

A digraph is supereulerian if it contains a spanning eulerian subdigraph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomasse and the first author: if the arc-connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.

Arc-Disjoint Paths in Decomposable Digraphs

We prove that the weak k-linkage problem is polynomial for every fixed k for totally i¾?-decomposable digraphs, under appropriate hypothesis on i¾?. We then apply this and recent results by Fradkin and Seymour on the weak k-linkage problem for digraphs of bounded independence number or bounded cut-width to get polynomial algorithms for some classes of digraphs like quasi-transitive digraphs, extended semicomplete digraphs, locally semicomplete digraphs all of which contain the class of semicomplete digraphs as a subclass and directed cographs.

Vertex-disjoint directed and undirected cycles in general digraphs

The dicycle transversal number τ(D) of a digraph D is the minimum size of a dicycle transversal of D, i.e. a set T⊆V(D) such that D−T is acyclic. We study the following problem: Given a digraph D, decide if there is a dicycle B in D and a cycle C in its underlying undirected graph UG(D) such that V(B)∩V(C)=∅. It is known that there is a polynomial time algorithm for this problem when restricted to strongly connected graphs, which actually finds B, C if they exist. We generalize this to any class of digraphs D with either τ(D)≠1 or τ(D)=1 and a bounded number of dicycle transversals, and show that the problem is NP-complete for a special class of digraphs D with τ(D)=1 and, hence, in general.

Process Integration Solutions for Water Networks in Integrated Steel Making Plants

Process Integration capabilities of promoting the internal recycling and reuse of material and energy streams allow reaching the goals of sustainable processing. Water is one of the main industrial resource which use has to be optimised to decrease freshwater intake and wastewater blowdown. Preliminary studies on the feasibility of different options are developed through Process Modelling and Simulation to predict process behaviour before plants conversion. The paper presents the approach to the problem of water reuse for an Italian integrated steelmaking plant. Application to a real case has been developed, related to reuse of continuous casting wastewater blowdown in basic oxygen steelmaking gas washing system. Process Modelling with main assumptions and results are described. The option is promising, as it involves a reduction of fresh water drawing up to 33 %, with changes in blowdown features of 2 % for pH value increase and 13 % for electrical conductivity reduction at constant global mass balance.

Quasi-hamiltonian paths in semicomplete multipartite digraphs

A quasi-hamiltonian path in a semicomplete multipartite digraph D is a path which visits each maximal independent set (also called a partite set) of D at least once. This is a generalization of a hamiltonian path in a tournament. In this paper we investigate the complexity of finding a quasi-hamiltonian path, in a given semicomplete multipartite digraph, from a prescribed vertex x to a prescribed vertex y as well as the complexity of finding a quasi-hamiltonian path whose end vertices belong to a given set of two vertices {x,y}. While both of these problems are polynomially solvable for semicomplete digraphs (here all maximal independent sets have size one), we prove that the first problem is NP-complete and describe a polynomial algorithm for the latter problem.

A Dive into the Specific Electric Energy Consumption in Steelworks

The paper describes an application of optimization techniques for the minimization of the specific electrical energy consumption related to the production of steel for a steelworks situated in Italy. The major electrical consumption derives from two internal plants: the Electric Arc Furnace and the Ladle Furnace. This work addresses the problem of understanding the best settings (based on predefined models) to produce a specific steel, which is mainly characterized by its steelgrade and quality, with the minimum energy consumption.

A Bin Packing Algorithm for Steel Production

The paper presents a novel method for steel cutting optimization, which is performed by means of a two dimensional bin packing algorithm, with bins of different sizes. Our model extends previous mixed integer programs for bin packing, accounting for many of the issues arising in the steel manufacturing industry. In particular the proposed method can satisfy customer requirements on product quality. The developed algorithm can also deal with parameters variability occurring after the rolling processes. The final problem is formulated as a mixed integer non linear program (MINLP). This model directly applies to steel cutting, but it can be easily adapted in all of its parts, or just some of them, to other (industrial) rectangular cutting problems on different surfaces.

Arc‐Disjoint Directed and Undirected Cycles in Digraphs

The dicycle transversal number of a digraph D is the minimum size of a dicycle transversal of D, that is a set of vertices of D, whose removal from D makes it acyclic. An arc a of a digraph D with at least one cycle is a transversal arc if a is in every directed cycle of D (making acyclic). In [3] and [4], we completely characterized the complexity of following problem: Given a digraph D, decide if there is a dicycle B in D and a cycle C in its underlying undirected graph such that . It turns out that the problem is polynomially solvable for digraphs with a constantly bounded number of transversal vertices (including cases where ). In the remaining case (allowing arbitrarily many transversal vertices) the problem is NP-complete. In this article, we classify the complexity of the arc-analog of this problem, where we ask for a dicycle B and a cycle C that are arc-disjoint, but not necessarily vertex-disjoint. We prove that the problem is polynomially solvable for strong digraphs and for digraphs with a constantly bounded number of transversal arcs (but possibly an unbounded number of transversal vertices). In the remaining case (allowing arbitrarily many transversal arcs) the problem is NP-complete.