Small Polygon Compression For Integer Coordinates

Abstract

We describe several polygon compression techniques to enable efficient transmission of polygons representing geographical targets. The main application is to embed compressed polygons to emergency alert messages that have strict length restrictions, as in the case of Wireless Emergency Alert messages. We are able to compress polygons to between 9.7% and 23.6% of original length, depending on characteristics of the specific polygons, reducing original polygon lengths from 43-331 characters to 8-55 characters. The best techniques apply several heuristics to perform initial compression, and then other algorithmic techniques, including higher base encoding. Further, these methods are respectful of computation and storage constraints typical of cell phones. Two of the best techniques include a \enquote{bignum} quadratic combination of integer coordinates and a variable length encoding, which takes advantage of a strongly skewed polygon coordinate distribution. Both techniques applied to one of two \enquote{delta} representations of polygons are on average able to reduce the size of polygons by some 80%. A repeated substring dictionary can provide further compression, and a merger of these techniques into a \enquote{polyalgorithm} can also provide additional improvements.