A TIGHT UPPER BOUND FOR GROUP-TESTING IN GRAPHS

Let e(G) denote the edge number of a graph G, and let t(G) be the worst-case number of tests required for finding a ''defective edge'' in G via group testing. This parameter has been intensively studied by several authors. The best general upper bound known before was t(G) less-than-or-equal-to inverted right perpendicular log2 e(G) inverted left perpendicular + 3. Here we prove t(G) less-than-or-equal-to inverted right perpendicular log2 e(G) inverted left perpendicular + 1. This result is tight in the sense that there exist infinitely many graphs with t(G) = inverted right perpendicular log2 e(G) inverted left perpendicular + 1. Moreover, our proof leads to a surprisingly simple efficient algorithm which computes for input G a test strategy needing at most inverted right perpendicular log2 e(G) inverted left perpendicular + 1 tests.