Optimal Compression of a Polyline with Segments and Arcs
  This paper describes an efficient approach to constructing a resultant polyline with a minimum number of segments and arcs. While fitting an arc can be done with complexity O(1) (see [1] and [2]), the main complexity is in checking that the resultant arc is within the specified tolerance. There are additional tests to check for the ends and for changes in direction (see [3, section 3] and [4, sections II.C and II.D]). However, the most important part in reducing complexity is the ability to subdivide the polyline in order to limit the number of arc fittings [2]. The approach described in this paper finds a compressed polyline with a minimum number of segments and arcs. 
Alexander Gribov
cs.CG