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
Optimal query complexity bounds for finding graphs
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Near-Optimal Sparse Recovery in the L1 Norm
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Optimally reconstructing weighted graphs using queries
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Toward a deterministic polynomial time algorithm with optimal additive query complexity
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
IEEE Transactions on Information Theory
Bounds on the performance of protocols for a multiple-access broadcast channel
IEEE Transactions on Information Theory
| Hi-index | 5.23 |
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 weighings for identifying the counterfeit coins and their weights is at least @W(mlognlogm). We give a deterministic polynomial time adaptive algorithm for identifying the counterfeit coins and their weights using O(mlognlogm+mloglogm) weighings, assuming that the weight of the counterfeit coins are greater than the weight of the authentic coins. This algorithm is optimal when m@?n^c^/^l^o^g^l^o^g^n, where c is any constant. Also our weighing complexity is within loglogm 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 H. Mazzawi (2008) [20], we get a similar positive result for the problem of reconstructing a hidden weighted graph using additive queries.