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
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
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
Topology discovery of sparse random graphs with few participants
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Topology discovery of sparse random graphs with few participants
ACM SIGMETRICS Performance Evaluation Review - Performance evaluation review
Toward a deterministic polynomial time algorithm with optimal additive query complexity
Theoretical Computer Science
Graph reconstruction via distance oracles
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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In this paper, we consider the problem of reconstructing a hidden graph with m edges using additive queries. Given a graph G = (V, E) and a set of vertices S ⊆ V, an additive query, Q(S), asks for the number of edges in the subgraph induced by S. The information theoretic lower bound for the query complexity of reconstructing a graph with n vertices and m edges is [EQUATION] In this paper we give the first polynomial time algorithm with query complexity that matches this lower bound1. This solves the open problem by [S. Choi and J. Han Kim. Optimal Query Complexity Bounds for Finding Graphs. STOC, 749--758, 2008]. In the paper, we actually show an algorithm for the generalized problem of reconstructing weighted graphs. In the weighted case, an additive query, Q(S), asks for the sum of weights of edges in the subgraph induces by S. The complexity of the algorithm also matches the information theoretic lower bound.