Binary robust positioning patterns with low redundancy and efficient locating algorithms

A robust positioning pattern is a large array that allows a mobile device to locate its position by reading a possibly corrupted small window around it. This paper provides constructions of binary positioning patterns, equipped with efficient locating algorithms, that are robust to a constant number of errors and have redundancy within a constant factor of optimality. Our construction of binary robust positioning sequences has the least known redundancy amongst those explicit constructions with efficient locating algorithms. On the other hand, for binary robust positioning arrays, our construction is the first explicit construction whose redundancy is within a constant factor of optimality. The locating algorithms accompanying our constructions run in time cubic in sequence length or array dimensions.