TY - JOUR

T1 - On lower bounds for selectinc the median

AU - Dor, Dorit

AU - Håstad, Johan

AU - Ulfberg, Staffan

AU - Zwick, Uri

PY - 2001/5

Y1 - 2001/5

N2 - We present a reformulation of the 2n + o(n) lower bound of Bent and John [Proceedings of the 17th Annual ACM Symposium on Theory of Computing, 1985, pp. 213-216] for the number of comparisons needed for selecting the median of n elements. Our reformulation uses a weight function. Apart from giving a more intuitive proof for the lower bound, the new formulation opens up possibilities for improving it. We use the new formulation to show that any pair-forming median finding algorithm, i.e., a median finding algorithm that starts by comparing [n/2] disjoint pairs of elements must perform, in the worst case, at least 2.01n + o(n) comparisons. This provides strong evidence that selecting the median requires at least cn + o(n) comparisons for some c > 2.

AB - We present a reformulation of the 2n + o(n) lower bound of Bent and John [Proceedings of the 17th Annual ACM Symposium on Theory of Computing, 1985, pp. 213-216] for the number of comparisons needed for selecting the median of n elements. Our reformulation uses a weight function. Apart from giving a more intuitive proof for the lower bound, the new formulation opens up possibilities for improving it. We use the new formulation to show that any pair-forming median finding algorithm, i.e., a median finding algorithm that starts by comparing [n/2] disjoint pairs of elements must perform, in the worst case, at least 2.01n + o(n) comparisons. This provides strong evidence that selecting the median requires at least cn + o(n) comparisons for some c > 2.

KW - Comparison algorithms

KW - Lower bounds

KW - Median selection

UR - http://www.scopus.com/inward/record.url?scp=18044399970&partnerID=8YFLogxK

U2 - 10.1137/S0895480196309481

DO - 10.1137/S0895480196309481

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AN - SCOPUS:18044399970

SN - 0895-4801

VL - 14

SP - 299

EP - 311

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 3

ER -