The Method of Tracking Domains in Search Problems

Simple search games on an infinite circular cylinder

“…sin A Ikgl <__ --7-(this condition prevents the effect of a thin tracing area that increases the set of points unattainable for the object B [9]). …”

“…w Detection conditions on the cylinder Let r be the radius of the directing circle of cylinder C. In [7], [9] it was shown that successful search (detection) is possible, if either l _> ~rr (1) (the corresponding trajectory of the searching object A is a ruling of the cylinder) or if the two following conditions:…”

“…The geometric method (the method of tracing areas) used in this work and based on the use of certain auxiliary sets that change in time is one of the approaches that have been developed just recently ( [7][8][9][10][11]), although some elements of the geometric approach can be found in [12].…”

“…It is convenient to assume that at any moment of time the object A is at the center of a circle of radius l forbidden for B. This circle will be called the control l-circle or just the control circle.w Tracing areaIn [7][8][9][10][11], it was shown that the investigation of search problems in the setting described above quite naturally leads to a class of sets of variable structure containing the control/-circle and free of the eluding object B. These auxiliary sets, called tracing area~ are constructed from a given trajectory of A and combine two components, namely the set of points that the eluding object B has no time to reach at a given moment of time (the af'termath area) and the set of points that B has no time to leave (the no-e~cape area).…”

Geometry of search problems with informational discrimination

“…In this work, we will concentrate our attention on the description (formulation and justification) of conditions whose fulfillment guarantees a successful search (detection) with the use of the results published in [18][19][20][21][22][23][24][25][26][27][28].…”