We present a comprehensive complexity analysis of an e cient algorithm for polynomial factorization in Z[x]. ? Supported by NSF 0728853 Complexity of Factoring A. Novocin, M. van Hoeij, W. Hart 1 This document is a work in progress. The central problem we address is the factorization of a square-free and monic polynomial in Z[x]. Forgoing for the moment any introduction to the method or explana...

In the trace reconstruction problem , an unknown source string x ∈ {0, 1} n is sent through a probabilistic deletion channel which independently deletes each bit with probability δ and concatenates surviving bits, yielding of . The to reconstruct given independent traces. This has received much attention in recent years both worst-case setting where may be arbitrary [DOS19, NP17, HHP18, HL20, C...

The traveling salesman problem (TSP) is a well-known optimization problem in graph theory, as well as in operations research that has nowadays received much attention because of its practical applications in industrial and service problems. In this problem, a salesman starts to move from an arbitrary place called depot and after visits all of the nodes, finally comes back to the depot. The obje...