Combinatorial search
Reconstructing a Hamiltonian cycle by querying the graph: application to DNA physical mapping
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
On the Power of Additive Combinatorial Search Model
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
The Journal of Machine Learning Research
Optimal query complexity bounds for finding graphs
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Learning and Verifying Graphs Using Queries with a Focus on Edge Counting
ALT '07 Proceedings of the 18th international conference on Algorithmic Learning Theory
Reconstructing weighted graphs with minimal query complexity
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Optimally reconstructing weighted graphs using queries
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Combinatorial search on graphs motivated by bioinformatics applications: a brief survey
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
IEEE Transactions on Information Theory
Toward a deterministic polynomial time algorithm with optimal additive query complexity
Theoretical Computer Science
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In this paper, we study two combinatorial search problems: The coin weighing problem with a spring scale (also known as the vector reconstructing problem using additive queries) and the problem of reconstructing weighted graphs using additive queries. Suppose we are given n identical looking coins. Suppose that m out of the n coins are counterfeit and the rest are authentic. Assume that we are allowed to weigh subsets of coins with a spring scale. It is known that the optimal number of weighing for identifying the counterfeit coins and their weights is at least Ω (m log n/log m). We give a deterministic polynomial time adaptive algorithm 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 coins are greater than the weight of the authentic coin. This algorithm is optimal when m ≤ nc/log log n, where c is any constant. Also our weighing complexity is within log log m times the optimal complexity for all m. To obtain this result, our algorithm makes use of search matrices, the divide and conquer approach and the guess and check approach. When combining these methods with the technique introduced in [Optimally Reconstructing Weighted Graphs Using Queries. SODA, 2010], we get a similar positive result for the problem of reconstructing a hidden weighted graph using additive queries.