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This paper considers a generalized version of the coin weighing problem witha spring scale that lies at the intersection of group testing and compressedsensing problems. Given a collection of $n\geq 2$ coins of total weight $d$(for a known integer $d$), where the weight of each coin is an unknown integerin the range of $\{0,1,\dots,k\}$ (for a known integer $k\geq 1$), the problemis to determine the weight of each coin by weighing subsets of coins in aspring scale. The goal is to minimize the average number of weighings over allpossible weight configurations. For $d=k=1$, an adaptive bisecting weighingstrategy is known to be optimal. However, even the case of $d=k=2$, which isthe simplest non-trivial case of the problem, is still open. For this case, wepropose and analyze a simple and effective adaptive weighing strategy. Anumerical evaluation of the exact recursive formulas, derived for the analysisof the proposed strategy, shows that this strategy requires about ${1.365\log_2n -0.5}$ weighings on average. To the best of our knowledge, this is the firstnon-trivial achievable upper bound on the minimum expected required number ofweighings for the case of $d=k=2$. As $n$ grows unbounded, the proposedstrategy, when compared to an optimal strategy within the commonly-used classof nested strategies, requires about $31.75\%$ less number of weighings onaverage; and in comparison with the information-theoretic lower bound, itrequires at most about $8.16\%$ extra number of weighings on average.

A Simple and Efficient Strategy for the Coin Weighing Problem with a Spring Scale