arXiv subjects

Lorenzo Balzotti

Publications and source records attributed to Lorenzo Balzotti.

9 recordsLinked to original sources

arXiv2026

Entity Resolution via Batched Oracle Queries

We consider an oracle that processes a limited batch of records at a time and clusters those that refer to the same real-world entity. We study how to interrogate such an oracle to resolve entities in a dataset whose size is far larger than a single batch, and where no batch is guaranteed to contain all records of any given entity. We aim at a pay-as-you-go approach, to have full control over the costs (the number of oracle consults), while achieving the highest possible recall at every step. We formally cast this problem as batched entity resolution, prove that selecting optimal batches is NP-hard, and provide an optimal solution under a natural condition on entity sizes. Finally, we evaluate our approach on six datasets and show its superiority over state-of-the-art baselines.

cs.DB↗

arXiv2025

Simpler and Unified Recognition Algorithm for Path Graphs and Directed Path Graphs

A path graph is the intersection graph of paths in a tree. A directed path graph is the intersection graph of paths in a directed tree. Even if path graphs and directed path graphs are characterized very similarly, their recognition algorithms differ widely. We further unify these two graph classes by presenting the first recognition algorithm for both path graphs and directed path graphs. We deeply use a recent characterization of path graphs, and we extend it to directed path graphs. Our algorithm does not require complex data structures and has an easy and intuitive implementation, simplifying recognition algorithms for both graph classes.

cs.DS↗

arXiv2022

How Vulnerable is an Undirected Planar Graph with respect to Max Flow

We study the problem of computing the vitality of edges and vertices with respect to the $st$-max flow in undirected planar graphs, where the vitality of an edge/vertex is the $st$-max flow decrease when the edge/vertex is removed from the graph. This allows us to establish the vulnerability of the graph with respect to the $st$-max flow. We give efficient algorithms to compute an additive guaranteed approximation of the vitality of edges and vertices in planar undirected graphs. We show that in the general case high vitality values are well approximated in time close to the time currently required to compute $st$-max flow $O(n\log\log n)$. We also give improved, and sometimes optimal, results in the case of integer capacities. All our algorithms work in $O(n)$ space.

cs.DS↗

arXiv2022

Non-Crossing Shortest Paths are Covered with Exactly Four Forests

Given a set of paths $P$ we define the \emph{Path Covering with Forest Number} of $P$} (PCFN($P$)) as the minimum size of a set $F$ of forests satisfying that every path in $P$ is contained in at least one forest in $F$. We show that PCFN($P$) is treatable when $P$ is a set of non-crossing shortest paths in a plane graph or subclasses. We prove that if $P$ is a set of non-crossing shortest paths of a planar graph $G$ whose extremal vertices lie on the same face of $G$, then PCFN($P$)\leq 4$, and this bound is tight.

math.CO↗

arXiv2022

Two New Characterizations of Path Graphs

Path graphs are intersection graphs of paths in a tree. We start from the characterization of path graphs by Monma and Wei [C.L.~Monma,~and~V.K.~Wei, Intersection Graphs of Paths in a Tree, J. Combin. Theory Ser. B, 41:2 (1986) 141--181] and we reduce it to some 2-colorings subproblems, obtaining the first characterization that directly leads to a polynomial recognition algorithm. Then we introduce the collection of the attachedness graphs of a graph and we exhibit a list of minimal forbidden 2-edge colored subgraphs in each of the attachedness graph.

math.CO↗

arXiv2022

A Linear Time Algorithm for Computing Max-Flow Vitality in Undirected Unweighted Planar Graphs

The vitality of an edge in a graph with respect to the maximum flow between two fixed vertices $s$ and $t$ is defined as the reduction of the maximum flow value caused by the removal of that edge. The max-flow vitality problem has already been efficiently solved for $st$-planar graphs but has remained open for general planar graphs. For the first time our result provides an optimal solution for general planar graphs although restricted to the case of unweighted planar graphs.

cs.DS↗

arXiv2022

Computing Lengths of Non-Crossing Shortest Paths in Planar Graphs

Given a plane undirected graph $G$ with non-negative edge weights and a set of $k$ terminal pairs on the external face, it is shown in Takahashi et al. (Algorithmica, 16, 1996, pp. 339-357) that the union $U$ of $k$ non-crossing shortest paths joining the $k$ terminal pairs (if they exist) can be computed in $O(n\log n)$ time, where $n$ is the number of vertices of $G$. In the restricted case in which the union $U$ of the shortest paths is a forest, it is also shown that their lengths can be computed in the same time bound. We show in this paper that it is always possible to compute the lengths of $k$ non-crossing shortest paths joining the $k$ terminal pairs in linear time, once the shortest paths union $U$ has been computed, also in the case $U$ contains cycles. Moreover, each shortest path $π$ can be listed in $O(\max\{\ell, \ell \log\frac{k}{\ell} \})$, where $\ell$ is the number of edges in $π$. As a consequence, the problem of computing non-crossing shortest paths and their lengths in a plane undirected weighted graph can be solved in $O(n\log k)$ time in the general case.

cs.DS↗

arXiv2022

Non-Crossing Shortest Paths in Undirected Unweighted Planar Graphs in Linear Time

Given a set of well-formed terminal pairs on the external face of an undirected planar graph with unit edge weights, we give a linear-time algorithm for computing the union of non-crossing shortest paths joining each terminal pair, where well-formed means that such a set of non-crossing paths exists. This allows us to compute distances between each terminal pair, within the same time bound. We also give a novel concept of incremental shortest path subgraph of a planar graph, i.e., a partition of the planar embedding in subregions that preserve distances, that can be of interest itself.

cs.DS↗

arXiv2021

A New Characterization of Path Graphs

Path graphs are intersection graphs of paths in a tree.~In this paper we give a "6\ good characterization" of path graphs, namely, we prove that path graph membership is in $NP\cap CoNP$ without resorting to existing polynomial time algorithms. The characterization is given in terms of the collection of the \emph{attachedness graphs} of a graph, a novel device to deal with the connected components of a graph after the removal of clique separators. On the one hand, the characterization refines and simplifies the characterization of path graphs due to Monma and Wei [C.L.~Monma,~and~V.K.~Wei, Intersection {G}raphs of {P}aths in a {T}ree, J. Combin. Theory Ser. B, 41:2 (1986) 141--181], which we build on, by reducing a constrained vertex coloring problem defined on the \emph{attachedness graphs} to a vertex 2-coloring problem on the same graphs. On the other hand, the characterization allows us to exhibit two exhaustive lists of obstructions to path graph membership in the form of minimal forbidden induced/partial 2-edge colored subgraphs in each of the \emph{attachedness graphs}.

cs.DM↗