## Reconstructing Sets From Interpoint Distances (2002)

by
Paul Lemke
,
Steven S. Skiena
,
Warren D. Smith

Venue: | of Algorithms Combin |

Citations: | 11 - 0 self |

### BibTeX

@TECHREPORT{Lemke02reconstructingsets,

author = {Paul Lemke and Steven S. Skiena and Warren D. Smith},

title = {Reconstructing Sets From Interpoint Distances},

institution = {of Algorithms Combin},

year = {2002}

}

### OpenURL

### Abstract

Which point sets realize a given distance multiset? Interesting cases include the "turnpike problem" where the points lie on a line, the "beltway problem" where the points lie on a loop, and multidimensional versions. We are interested both in the algorithmic problem of determining such point sets for a given collection of distances and the combinatorial problem of finding bounds on the maximum number of different solutions. These problems have applications in genetics and crystallography.