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We study the classical problem introduced by R. Isaacs and S. Gal ofminimizing the time to find a hidden point $H$ on a network $Q$ moving from aknown starting point. Rather than adopting the traditional continuous unitspeed path paradigm, we use the ``expanding search'' paradigm recentlyintroduced by the authors. Here the regions $S\left( t\right) $ that have beensearched by time $t$ are increasing from the starting point and have totallength $t$. Roughly speaking the search follows a sequence of arcs $a_{i}$ suchthat each one starts at some point of an earlier one. This type of search isoften carried out by real life search teams in the hunt for missing persons,escaped convicts, terrorists or lost airplanes. The paper which introduced thistype of search solved the adversarial problem (where $H$ is hidden to take along time to find) for the cases where $Q$ is a tree or is 2-arc-connected.This paper solves the game on some additional families of networks. However themain contribution is to give strategy classes which can be used on any networkand have expected search times which are within a factor close to 1 of thevalue of the game (minimax search time). We identify cases where our strategiesare in fact optimal.

Constant Factor Approximate Solutions for Expanding Search on General Networks