# A Greedy Heuristic for the Rectilinear Steiner Tree Problem

### Marshall W. Bern and Marcio de Carvalho

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-87-306

September 1986

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1987/CSD-87-306.pdf

Clark Thompson recently suggested a very natural "greedy" heuristic for the rectilinear Steiner problem (RSP), analogous to Kruskal's algorithm for the minimum spanning tree problem. We study this heuristic by comparing the solutions it finds with rectilinear minimum spanning trees. We first prove a theoretical result on instances of RSP consisting of a large number of random points in the unit square. Thompson's heuristic produces a tree of expected length some fraction shorter than a minimum spanning tree. The second part of this paper studies Thompsons's heuristic experimentally and finds that it gives solutions about 9% shorter than minimum spanning trees on medium size problems (40-100 nodes). This performance is very similar to that of other RSP heuristics described in the literature.

BibTeX citation:

@techreport{Bern:CSD-87-306, Author = {Bern, Marshall W. and de Carvalho, Marcio}, Title = {A Greedy Heuristic for the Rectilinear Steiner Tree Problem}, Institution = {EECS Department, University of California, Berkeley}, Year = {1986}, Month = {Sep}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1986/6114.html}, Number = {UCB/CSD-87-306}, Abstract = {Clark Thompson recently suggested a very natural "greedy" heuristic for the rectilinear Steiner problem (RSP), analogous to Kruskal's algorithm for the minimum spanning tree problem. We study this heuristic by comparing the solutions it finds with rectilinear minimum spanning trees. We first prove a theoretical result on instances of RSP consisting of a large number of random points in the unit square. Thompson's heuristic produces a tree of expected length some fraction shorter than a minimum spanning tree. The second part of this paper studies Thompsons's heuristic experimentally and finds that it gives solutions about 9% shorter than minimum spanning trees on medium size problems (40-100 nodes). This performance is very similar to that of other RSP heuristics described in the literature.} }

EndNote citation:

%0 Report %A Bern, Marshall W. %A de Carvalho, Marcio %T A Greedy Heuristic for the Rectilinear Steiner Tree Problem %I EECS Department, University of California, Berkeley %D 1986 %@ UCB/CSD-87-306 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1986/6114.html %F Bern:CSD-87-306