# Optimal Algorithms for the Coin Weighing Problem with a Spring Scale

@inproceedings{Bshouty2009OptimalAF, title={Optimal Algorithms for the Coin Weighing Problem with a Spring Scale}, author={Nader H. Bshouty}, booktitle={COLT}, year={2009} }

Suppose we are given n coins out of a collection of coins of two distinct weights w0 and w1, true and counterfeit coins, respectively, where d of them are counterfeit coins. [...] Key Method This algorithm is based on a new optimal adaptive algorithm for reconstructing bounded weight vectors in polynomial time. This solves the general problem of learning any linear function with bounded integer coefficient in polynomial time with optimal number of substitution queries. To the best of our knowledge all the… Expand

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Toward a Deterministic Polynomial Time Algorithm with Optimal Additive Query Complexity

- Mathematics, Computer Science
- MFCS
- 2010

A deterministic polynomial time adaptive algorithm is given for identifying the counterfeit coins and their weights using O (m log n/log m + m log log m) weighings, assuming that the weight of the counterfeit coin are greater than the Weight of the authentic coin. Expand

Toward a deterministic polynomial time algorithm with optimal additive query complexity

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2012

A deterministic polynomial time adaptive algorithm is given for identifying the counterfeit coins and their weights using O(mlognlogm+mloglogm) weighings, assuming that the weight of the counterfeiting coins are greater than theWeight of the authentic coins. Expand

Algorithms for the Coin Weighing Problems with the Presence of Noise

- Computer Science, Mathematics
- Electron. Colloquium Comput. Complex.
- 2011

A non-adaptive polynomial time algorithm that does O(n/ log n) weighings and detect the counterfeit coins even if n of the answers of the weighings received are incorrect or missing for any constant c < 1. Expand

Searching for a subset of counterfeit coins: Randomization vs determinism and adaptiveness vs non-adaptiveness

- Mathematics, Computer Science
- Random Struct. Algorithms
- 2013

While for randomized algorithms queries are sufficient, the deterministic non-adaptive counterpart still requires Θ(klog k +1(n/k) queries, in case k ≤ n/28; therefore, finding any subset of defectives is not easier than finding all of them by a non- Adaptive deterministic algorithm. Expand

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

- Computer Science, Mathematics
- 2018 IEEE International Symposium on Information Theory (ISIT)
- 2018

This paper considers a generalized version of the coin weighing problem with a spring scale that lies at the intersection of group testing and compressed sensing problems and proposes and analyzes a simple and effective adaptive weighing strategy. Expand

Polynomial Time Optimal Query Algorithms for Finding Graphs with Arbitrary Real Weights

- Mathematics, Computer Science
- COLT
- 2013

The rst polynomial time algorithms with optimal query complexity for the general class of graphs with n vertices and at most m edges in which the weights of edges are arbitrary real numbers are constructed. Expand

The Deterministic and Randomized Query Complexity of a Simple Guessing Game

- Computer Science, Mathematics
- Electron. Colloquium Comput. Complex.
- 2012

By using randomization Paul can find the secret code with an expected number of O(n log log n) queries, which is optimal by matching it with a lower bound of the same asymptotic magnitude. Expand

On the Coin Weighing Problem with the Presence of Noise

- Mathematics, Computer Science
- APPROX-RANDOM
- 2012

This paper considers the following coin weighing problem: given n coins for which some of them are counterfeit with the same weight, how to detect the counterfeit coins a with minimal number of weighings. Expand

The Query Complexity of Finding a Hidden Permutation

- Mathematics, Computer Science
- Space-Efficient Data Structures, Streams, and Algorithms
- 2013

This work proves matching upper and lower bounds for the deterministic and randomized query complexity of Θ(n logn) and Θ (n loglogn), respectively. Expand

ApSimon's Mint Problem with Three or More Weighings

- Mathematics
- 2014

ApSimon considered the problem of deciding by a process of two weighings on which of a known number of mints emit either coins of a known genuine weight or emit coins of a different secondary but… Expand

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