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Two fundamental algorithm-design paradigms are Tree Search and Dynamic Programming. The techniques used therein have been shown to complement one another when solving the complete set partitioning problem, also known as the coalition…
When we deal with a matroid ${\mathcal M}=(U,{\mathcal I})$, we usually assume that it is implicitly given by means of the independence (IND) oracle. Time complexity of many existing algorithms is polynomially bounded with respect to $|U|$…
Let G be a planar graph and F a set of additional edges not yet in G. The multiple edge insertion problem (MEI) asks for a drawing of G+F with the minimum number of pairwise edge crossings, such that the subdrawing of G is plane. Finding an…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
We present an exact and complete algorithm to isolate the real solutions of a zero-dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination method which improves upon existing approaches in a number of…
We provide proofs certifying that the structure theorem for vertex sets of bounded bidimensionality holds with polynomial bounds. The bidimensionality of vertex sets is a common generalisation of both treewidth and the face-cover-number of…
Schubert polynomials are a basis for the polynomial ring that represent Schubert classes for the flag manifold. In this paper, we introduce and develop several new combinatorial models for Schubert polynomials that relate them to other…
Graph neural networks have been successful in many learning problems and real-world applications. A recent line of research explores the power of graph neural networks to solve combinatorial and graph algorithmic problems such as subgraph…
In this paper, we present an improved numerical algorithm for computing the intersection area of multiple circles and a complex polygon efficiently. This geometric problem is fundamental to applications such as wireless sensor networks and…
The {\sc Directed Maximum Leaf Out-Branching} problem is to find an out-branching (i.e. a rooted oriented spanning tree) in a given digraph with the maximum number of leaves. In this paper, we improve known parameterized algorithms and…
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…
We present an improved algorithm for computing the $4$-edge-connected components of an undirected graph in linear time. The new algorithm uses only elementary data structures, and it is simple to describe and to implement in the pointer…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
We give two algorithms computing representative families of linear and uniform matroids and demonstrate how to use representative families for designing single-exponential parameterized and exact exponential time algorithms. The…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
We present an algorithm that enumerates all the minimal triangulations of a graph in incremental polynomial time. Consequently, we get an algorithm for enumerating all the proper tree decompositions, in incremental polynomial time, where…
We consider the multivariate interlace polynomial introduced by Courcelle (2008), which generalizes several interlace polynomials defined by Arratia, Bollobas, and Sorkin (2004) and by Aigner and van der Holst (2004). We present an…
Mayer's theory of cluster integrals allows one to write the partition function of a gas model as a generating function of weighted graphs. Recently, Labelle, Leroux and Ducharme have studied the graph weights arising from the…
Given a graph $G$, the maximal induced subgraphs problem asks to enumerate all maximal induced subgraphs of $G$ that belong to a certain hereditary graph class. While its optimization version, known as the minimum vertex deletion problem in…
The classical Menger's theorem states that in any undirected (or directed) graph $G$, given a pair of vertices $s$ and $t$, the maximum number of vertex (edge) disjoint paths is equal to the minimum number of vertices (edges) needed to…