A Simple Algorithm for Hamiltonicity release_yhd2qcvllbfe3mjarkg6mwx6qy

by Hasan Abasi, Nader H. Bshouty

Released as a article .



We develop a new algebraic technique that solves the following problem: Given a black box that contains an arithmetic circuit f over a field of characteristic 2 of degree d. Decide whether f, expressed as an equivalent multivariate polynomial, contains a multilinear monomial of degree d. This problem was solved by Williams W and Björklund et. al. BHKK for a white box (the circuit is given as an input) that contains arithmetic circuit. We show a simple black box algorithm that solves the problem with the same time complexity. This gives a simple randomized algorithm for the simple k-path problem for directed graphs of the same time complexity[O^*(f(k)) is O(poly(n)· f(k))] O^*(2^k) as in W and with reusing the same ideas from BHKK with the above gives another algorithm (probably not simpler) for undirected graphs of the same time complexity O^*(1.657^k) as in B10,BHKK.
In text/plain format

Archived Files and Locations

application/pdf  143.2 kB
web.archive.org (webarchive)
arxiv.org (repository)
Read Archived PDF
Type  article
Stage   submitted
Date   2014-04-10
Version   v1
Language   en ?
arXiv  1404.2827v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: d5ab0a89-7258-4338-a36d-eb43b1103f37