 
Summary: Economical Graph Discovery
Noga Alon
Yuval Emek
Michal Feldman§
Moshe Tennenholtz¶
Abstract
Consider a weighted nvertex, medge graph G with designated source s and destination t.
The topology of G is known, while the edge weights are hidden. Our goal is to discover either
the edge weights in the graph or a shortest (s, t)path. This is done by means of agents that
traverse different (s, t)paths in multiple rounds and report back the total cost they incurred.
Various cost models are considered, differing from each other in their approach to congestion
effects. We seek bounds on the number of rounds and the number of agents required to complete
the discovery of the edge weights or a shortest path.
A host of results concerning such bounds for both directed and undirected graphs are es
tablished. Among these results, we show that: (1) for undirected graphs, all edge weights can
be discovered within a single round consisting of m agents; (2) discovering a shortest path in
either undirected or directed acyclic graphs requires at least m  n + 1 agents; and (3) the edge
weights in a directed acyclic graph can be discovered in m rounds with m + n  2 agents under
congestionaware cost models. Our study introduces a new setting of graph discovery under
uncertainty and provides fundamental understanding of the problem.
