Fang, JCao, MingMorse, A StephenAnderson, Brian2015-12-100363-0129http://hdl.handle.net/1885/53654The sensor network localization problem with distance information is to determine the positions of all sensors in a network, given the positions of some of the sensors and the distances between some pairs of sensors. A definition is given for a sensor network in the plane to be "sequentially localizable." It is shown that the graph of a sequentially localizable network must have a "bilateration ordering," and a polynomial time algorithm is given for deciding whether or not a network's graph has such an ordering. A provably correct algorithm is given which consists of solving a sequence of quadratic equations, and it is shown that the algorithm can localize any localizable network in the plane whose graph has a bilateration ordering.Keywords: Distance informations; Localization; Polynomial-time algorithms; Quadratic equations; Sensor network localizations; Graph theory; Polynomial approximation; Programming theory; Rigidity; Sensors; Wireless sensor networks; Sensor networks Graph theory; Localization; Rigidity; Sensor networks200910.1137/0706811202016-02-24