Treasure hunt

A single deterministic agent starts at a node \(s\) of an unknown connected graph whose edges carry ports (at each node, local numbers of the edges at that node); a treasure sits at an unknown node \(v^*\) at distance \(d\) from \(s\). The agent must reach \(v^*\) (it recognises the treasure when it arrives). Cost is the number of moves (edge traversals) until the treasure is found, measured against \(d\), against \(e(d)\) (the number of edges with an endpoint at distance less than \(d\) from \(s\)) or against a path weight defined per paper. Help counts any external help the agent receives: bits of advice from an oracle that knows the instance, or pebbles (objects left on nodes) placed by it. Unless a variant says otherwise the agent knows nothing about the graph, \(d\) or \(v^*\).

Measures: Cost, edge traversals until the treasure is reached; Help, bits of advice, or pebbles placed in advance by an oracle.