A. Shapira

collaborators

11 papers

cs.DS2026

Graph k-Coloring in Average Sublinear Time

Cassandra Marcussen, Edward Pyne, Ronitt Rubinfeld +2

The paper presents an algorithm that colors k‑colorable graphs in expected O(nk) time, breaking the long‑standing quadratic average‑case barrier and achieving linear time for const…

math.NT2026

An Elementary Analysis of the Prime Partition Function

Asaf Cohen Antonir, Asaf Shapira

Let $pp (n)$ denote the number of ways to write $n$ as a sum of primes. In this paper, we show that $lo g pp (n) \sim 2 I ¨ \frac{n}{3 lo g n} .$ While sharper estimates ar…

math.CO2026

On Ramsey Properties of k-Majority Tournaments

Asaf Shapira, Raphael Yuster

A central objective in Ramsey theory is determining whether restricted families of discrete structures necessarily contain substantially larger homogeneous substructures, compared…

math.CO2026

Is it easy to regularize a hypergraph with easy links?

Lior Gishboliner, Asaf Shapira, Yuval Wigderson

A partition of a (hyper)graph is $ε$ -homogenous if the edge densities between almost all clusters are either at most $ε$ or at least $1 - ε$ . Suppose a…

cs.DS2025

Polynomial Property Testing

Lior Gishboliner, Asaf Shapira

Property testers are fast, randomized "election polling"-type algorithms that determine if an input (e.g., graph or hypergraph) has a certain property or is $ε$ -far from…

math.CO2025

Regularity for hypergraphs with bounded VC $_{2}$ dimension