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COCOON
2009
Springer
15 years 9 months ago
On Smoothed Analysis of Quicksort and Hoare's Find
We provide a smoothed analysis of Hoare’s find algorithm and we revisit the smoothed analysis of quicksort. Hoare’s find algorithm – often called quickselect – is an easy...
Mahmoud Fouz, Manfred Kufleitner, Bodo Manthey, Ni...
ENDM
2007
96views more  ENDM 2007»
15 years 3 months ago
Sub-Ramsey Numbers for Arithmetic Progressions and Schur Triples
For a given positive integer k, sr(m, k) denotes the minimal positive integer such that every coloring of [n], n ≥ sr(m, k), that uses each color at most k times, yields a rainb...
Jacob Fox, Veselin Jungic, Rados Radoicic
ISSAC
1997
Springer
194views Mathematics» more  ISSAC 1997»
15 years 7 months ago
The Minimised Geometric Buchberger Algorithm: An Optimal Algebraic Algorithm for Integer Programming
IP problems characterise combinatorial optimisation problems where conventional numerical methods based on the hill-climbing technique can not be directly applied. Conventional me...
Qiang Li, Yike Guo, Tetsuo Ida, John Darlington
MOC
2010
14 years 10 months ago
The number field sieve for integers of low weight
We define the weight of an integer N to be the smallest w such that N can be represented as w i=1 i2ci , with 1,..., w{1,-1}. Since arithmetic modulo a prime of low weight is parti...
Oliver Schirokauer
CPC
2008
66views more  CPC 2008»
15 years 3 months ago
B2[ g] Sets and a Conjecture of Schinzel and Schmidt
A set of integers A is called a B2[g] set if every integer m has at most g representations of the form m = a + a , with a a and a, a A. We obtain a new lower bound for F(g, n), t...
Javier Cilleruelo, Carlos Vinuesa