Geometry of coin-weighing problems

Noga Alon, Dmitry N. Kozlov, Van H. Vu

Research output: Contribution to journalConference articlepeer-review

9 Scopus citations

Abstract

Given a set of m coins out of a collection of coins of k unknown distinct weights, we wish to decide if all the m given coins have the same weight or not using the minimum possible number of weighings in a regular balance beam. Let m(n, k) denote the maximum possible number of coins for which the above problem can be solved in n weighings. We show that m(n, 2) = n( 1/2 +o(l))n, whereas for all 3≤k≤n+1, m(n, k) is much smaller than m(n, 2) and satisfies m(n, k) = Θ(n log n/log k). The proofs have an interesting geometric flavour, and combine Linear Algebra techniques with geometric, probabilistic and combinatorial arguments.

Original languageEnglish (US)
Pages (from-to)524-532
Number of pages9
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
StatePublished - 1996
Externally publishedYes
EventProceedings of the 1996 37th Annual Symposium on Foundations of Computer Science - Burlington, VT, USA
Duration: Oct 14 1996Oct 16 1996

All Science Journal Classification (ASJC) codes

  • Hardware and Architecture

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