Optimal query complexity bounds for finding graphs

We consider the problem of finding an unknown graph by using two types of queries with an additive property. Given a graph, an additive query asks the number of edges in a set of vertices while a cross-additive query asks the number of edges crossing between two disjoint sets of vertices. The queries ask sum of weights for the weighted graphs. These types of queries were partially motivated in DNA shotgun sequencing and linkage discovery problem of artificial intelligence.

Authors

• Sung-Soon Choi
• Jeong Han Kim

Keywords

• coin weighing problem
• combinatorial group testing
• combinatorial search
• fourier coefficient
• graph finding
• littlewood-offord theorem
• pseudo-boolean function