Related papers: Greedy algorithms and poset matroids
Many dynamic programming algorithms for discrete 0-1 optimizationproblems are "pure" in that their recursion equations only use min/max and addition operations, and do not depend on actual input weights. The well-known greedy algorithm of…
We present a formal analysis, in Isabelle/HOL, of optimisation algorithms for matroids, which are useful generalisations of combinatorial structures that occur in optimisation, and greedoids, which are a generalisation of matroids. Although…
Greedy minimum weight spanning tree packings have proven to be useful in connectivity-related problems. We study the process of greedy minimum weight base packings in general matroids and explore its applications. For general matroids, we…
We introduce a greedy algorithm optimizing arrangements of lines with respect to a property. We apply this algorithm to the case of simpliciality: it recovers all known simplicial arrangements of lines in a very short time and also produces…
The greedy algorithm adapted from Kruskal's algorithm is an efficient and folklore way to produce a $k$-spanner with girth at least $k+2$. The greedy algorithm has shown to be `existentially optimal', while it's not `universally optimal'…
A greedoid is a generalization of a matroid allowing for more flexible analyses and modeling of combinatorial optimization problems. However, these structures decimate many matroid properties contributing to their pervasive nature. A…
There has been an increasing interest in methods that exploit permutation reasoning to search for directed acyclic causal models, including the "Ordering Search" of Teyssier and Kohler and GSP of Solus, Wang and Uhler. We extend the methods…
Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…
We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that…
The greedy algorithm for approximating dominating sets is a simple method that is known to compute an $(\ln n+1)$-approximation of a minimum dominating set on any graph with $n$ vertices. We show that a small modification of the greedy…
This letter studies the problem of minimizing increasing set functions, or equivalently, maximizing decreasing set functions, over the base of a matroid. This setting has received great interest, since it generalizes several applied…
Greedy algorithms are a fundamental category of algorithms in mathematics and computer science, characterized by their iterative, locally optimal decision-making approach, which aims to find global optima. In this review, we will discuss…
We generalise a sparsity condition for hypergraphs and show a result relating sparseness of hypergraphs to the decomposition of a modified incidence graph into edge-disjoint forests. We also give new sparsity conditions for posets and…
We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. This leads to a characterization of chordal graphs…
An important problem in computational topology is to calculate the homology of a space from samples. In this work, we develop a statistical approach to this problem by calculating the expected rank of an induced map on homology from a…
For compressed sensing over arbitrarily connected networks, we consider the problem of estimating underlying sparse signals in a distributed manner. We introduce a new signal model that helps to describe inter-signal correlation among…
Whereas there are simple algorithms that are proven to be optimal for the Classical and the Multiple Choice Secretary Problem, the Matroid Secretary Problem is less thoroughly understood. This paper proposes the generalization of some…
Simplicial partitions are a fundamental structure in computational geometry, as they form the basis of optimal data structures for range searching and several related problems. Current algorithms are built on very specific spatial…
We define an independence system associated with simple graphs. We prove that the independence system is a matroid for certain families of graphs, including trees, with bases as minimal resolving sets. Consequently, the greedy algorithm on…
The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems (also known as Markushevich bases) in quasi-Banach spaces from a functional-analytic…