TY - JOUR

T1 - Matching nuts and bolts faster

AU - Alon, Noga

AU - Bradford, Phillip G.

AU - Fleischer, Rudolf

N1 - Funding Information:
” Corresponding author. Email: rudolf@mpi-sb.mpg.de. ’ A preliminary version of the paper was presented at ISAAC’95 151. 2 Email: noga@math.tau.ac.il. 3 Email: bradford@mpi-sb.mpg.de. 4The first author was supported in part by a USA Israeli BSF grant. The second and the thiid author were partially supported by the EU ESPRIT LTR Project No. 20244 (ALCOM-IT).

PY - 1996/8/12

Y1 - 1996/8/12

N2 - The problem of matching nuts and bolts is the following: Given a collection of n nuts of distinct sizes and n bolts such that there is a one-to-one correspondence between the nuts and the bolts, find for each nut its corresponding bolt. We can only compare nuts to bolts. That is we can neither compare nuts to nuts, nor bolts to bolts. This humble restriction on the comparisons appears to make this problem very hard to solve. In fact, the best explicit deterministic algorithm to date is due to Alon et al. (1994) and takes Θ(n log4) time. In this paper, we give a simpler O(n log2 n) time algorithm. The existence of an O (n log n) time algorithm has been proved recently (Bradford, 1995; Komlós et al., 1996).

AB - The problem of matching nuts and bolts is the following: Given a collection of n nuts of distinct sizes and n bolts such that there is a one-to-one correspondence between the nuts and the bolts, find for each nut its corresponding bolt. We can only compare nuts to bolts. That is we can neither compare nuts to nuts, nor bolts to bolts. This humble restriction on the comparisons appears to make this problem very hard to solve. In fact, the best explicit deterministic algorithm to date is due to Alon et al. (1994) and takes Θ(n log4) time. In this paper, we give a simpler O(n log2 n) time algorithm. The existence of an O (n log n) time algorithm has been proved recently (Bradford, 1995; Komlós et al., 1996).

KW - Analysis of algorithms

KW - Nuts and bolts

KW - Sorting

UR - http://www.scopus.com/inward/record.url?scp=0006670760&partnerID=8YFLogxK

U2 - 10.1016/0020-0190(96)00104-4

DO - 10.1016/0020-0190(96)00104-4

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AN - SCOPUS:0006670760

SN - 0020-0190

VL - 59

SP - 123

EP - 127

JO - Information Processing Letters

JF - Information Processing Letters

IS - 3

ER -