Related papers: Greedy balanced pairs in $N$-free ordered sets

The change-making problem consists of representing a certain amount of money with the least possible number of coins, from a given, pre-established set of denominations. The greedy algorithm works by choosing the coins of largest possible…

Any nonempty, compact, semi-algebraic set in [0, 1] n is the projection of the set of mixed equilibria of a finite game with 2 actions per player on its first n coordinates. A similar result follows for sets of equilibrium payoffs. The…

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and $f$ be a 0-1 labeling of $E(G)$ so that the absolute difference in the number of edges labeled 1 and 0 is no more than one. Call such a labeling $f$ \emph{edge-friendly}.…

This paper considers the classic Online Steiner Forest problem where one is given a (weighted) graph $G$ and an arbitrary set of $k$ terminal pairs $\{\{s_1,t_1\},\ldots ,\{s_k,t_k\}\}$ that are required to be connected. The goal is to…

We show that the K_1 group of a C*-algebra $A$ can be defined as homotopy classes of pairs, called balanced, of not necessarily unitary matrices over $A$ that have equal defects from being unitary. We also consider pairs of order zero…

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…

In this paper, motivated by the notion of $w$-Property $(A)$ defined in [2], we introduce the notions of $w$-left Property $(A)$ and $w$-right Property $(A)$. We also introduce the notions of $w$-partially greedy basis (using a…

We derive new results for the performance of a simple greedy algorithm for finding large independent sets and matchings in constant degree regular graphs. We show that for $r$-regular graphs with $n$ nodes and girth at least $g$, the…

In this paper, we consider a randomized greedy algorithm for independent sets in $r$-uniform $d$-regular hypergraphs $G$ on $n$ vertices with girth $g$. By analyzing the expected size of the independent sets generated by this algorithm, we…

This paper proposes a greedy algorithm named as Big step greedy set cover algorithm to compute approximate minimum set cover. The Big step greedy algorithm, in each step selects p sets such that the union of selected p sets contains…

The change-making problem was recently extended to sets of positive integers not containing the element $1$, and from there to numerical semigroups. A greedy numerical semigroup is defined as a numerical semigroup where the greedy…

An ordering of the vertices of a graph is \emph{connected} if every vertex (but the first) has a neighbor among its predecessors. The greedy colouring algorithm of a graph with a connected order consists in taking the vertices in order, and…

We study the fair allocation of indivisible goods across groups of agents, where each agent fully enjoys all goods allocated to their group. We focus on groups of two (couples) and other groups of small size. For two couples, an EF1…

A spanner graph on a set of points in $R^d$ contains a shortest path between any pair of points with length at most a constant factor of their Euclidean distance. In this paper we investigate new models and aim to interpret why good…

We study adaptive greedy algorithms for the problems of stochastic set cover with perfect and imperfect coverages. In stochastic set cover with perfect coverage, we are given a set of items and a ground set B. Evaluating an item reveals its…

Randomized greedy algorithms form one of the simplest yet most effective approaches for computing approximate matchings in graphs. In this paper, we focus on the class of vertex-iterative (VI) randomized greedy matching algorithms, which…

We show that the first-order logical theory of the binary overlap-free words (and, more generally, the ${\alpha}$-free words for rational ${\alpha}$, $2 < {\alpha} \leq 7/3$), is decidable. As a consequence, many results previously obtained…

A balanced graph is a bipartite graph with no induced circuit of length 2 mod 4. These graphs arise in linear programming. We focus on graph-algebraic properties of balanced graphs to prove a complete classification of balanced Cayley…

We show that the left-greedy algorithm is a better algorithm than the right-greedy algorithm for sorting permutations using t stacks in series when t>1. We also supply a method for constructing some permutations that can be sorted by t…

Let $S_{(x,y]} = \left\{\frac{p_n}{p_{n+1}-2} :~ n\in I \right\}$, where $I = \left\{n :~ x<p_n \le y \right\}$, $p_n$ is the $n$-th prime and $x, y \in \mathbb{R}_{>0}$. If $M_\alpha(x,y)$ denotes the $\alpha$-power mean of the elements of…