Related papers: Efficient coroutine generation of constrained Gray…

We give polynomial-time randomized algorithms for computing the girth and the cogirth of binary matroids that are low-rank perturbations of graphic matroids.

This paper deals with lattice congruences of the weak order on the symmetric group, and initiates the investigation of the cover graphs of the corresponding lattice quotients. These graphs also arise as the skeleta of the so-called…

In a finite undirected simple graph, a chordless cycle is an induced subgraph which is a cycle. A graph is called cyclically orientable if it admits an orientation in which every chordless cycle is cyclically oriented. We propose an…

We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives…

The recursive removal of leaves (dead end vertices) and their neighbors from an undirected network results, when this pruning algorithm stops, in a so-called core of the network. This specific subgraph should be distinguished from…

Gabidulin codes over fields of characteristic zero were recently constructed by Augot et al., whenever the Galois group of the underlying field extension is cyclic. In parallel, the interest in sparse generator matrices of Reed-Solomon and…

The Boltzmann model for the random generation of "decomposable" combinatorial structures is a set of techniques that allows for efficient random sampling algorithms for a large class of families of discrete objects. The usual requirement of…

The study of sorting permutations by block interchanges has recently been stimulated by a phenomenon observed in the genome maintenance of certain ciliate species. The result was the identification of a block interchange operation that…

We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using…

We present a general framework to generate trees every vertex of which has a non-negative weight and a color. The colors are used to impose certain restrictions on the weight and colors of other vertices. We first extend the enumeration…

Functional coroutines are a restricted form of control mechanism, where each coroutine is represented with both a continuation and an environment. This restriction was originally obtained by considering a constructive version of Parigot's…

This article introduces an algorithm to draw random discrete uniform variables within a given range of size n from a source of random bits. The algorithm aims to be simple to implement and optimal both with regards to the amount of random…

A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and…

We study the complexity of finding communication trees with the lowest possible completion time for rooted, irregular gather and scatter collective communication operations in fully connected, $k$-ported communication networks under a…

Large monolithic generative models trained on massive amounts of data have become an increasingly dominant approach in AI research. In this paper, we argue that we should instead construct large generative systems by composing smaller…

Graph-modification problems, where we modify a graph by adding or deleting vertices or edges or contracting edges to obtain a graph in a {\it simpler} class, is a well-studied optimization problem in all algorithmic paradigms including…

How can we train a statistical mixture model on a massive data set? In this work we show how to construct coresets for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also…

Treewidth is an important graph invariant, relevant for both structural and algorithmic reasons. A necessary condition for a graph class to have bounded treewidth is the absence of large cliques. We study graph classes closed under taking…

Graphs are extremely versatile and ubiquitous mathematical structures with potential to model a wide range of domains. For this reason, graph problems have been of interest since the early days of computer science. Some of these problems…

Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…