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Adversarial search of a network for an immobile Hider (or target) wasintroduced and solved for rooted trees by Gal (1979). In this zero-sum game, aHider picks a point to hide on the tree and a Searcher picks a unit speedtrajectory starting at the root. The payoff (to the Hider) is the search time.In Gal's model (and many subsequent investigations), the Searcher receives noadditional information after the Hider chooses his location. In reality, theSearcher will often receive such locational information. For homeland security,mobile sensors on vehicles have been used to locate radioactive materialstashed in an urban environment. In a military setting, mobile sensors candetect chemical signatures from land mines. In predator-prey search, thepredator often has specially attuned senses (hearing for wolves, vision foreagles, smell for dogs, sonar for bats, pressure sensors for sharks) that mayhelp it locate the prey. How can such noisy locational information be used bythe Searcher to modify her route? We model such information as signals whichindicate which of two branches of a binary tree should be searched first, wherethe signal has a known accuracy p<1. Our solution calculates which branch (atevery branch node) is favored, meaning it should always be searched first whenthe signal is in that direction. When the signal is in the other direction, wecalculate the probability the signal should be followed. Compared to theoptimal Hider strategy in the classic search game of Gal, the Hider's optimaldistribution for this model is more skewed towards leaf nodes that are furtherfrom the root.

Searching a Tree with Signals: Routing Mobile Sensors for Targets Emitting Radiation, Chemicals or Scents