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CAPS in Z(2,n)

Kurz, Sascha — 2009

Serdica Journal of Computing

We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear programming formulations and identify some values for small n.

On the Generation of Heronian Triangles

Kurz, Sascha — 2008

Serdica Journal of Computing

We describe several algorithms for the generation of integer Heronian triangles with diameter at most n. Two of them have running time O(n^(2+ε)). We enumerate all integer Heronian triangles for n ≤ 600000 and apply the complete list on some related problems.

Constructing 7-Clusters

Kurz, SaschaNoll, Landon CurtRathbun, RandallSimmons, Chuck — 2014

Serdica Journal of Computing

ACM Computing Classification System (1998): G.2, G.4. A set of n lattice points in the plane, no three on a line and no four on a circle, such that all pairwise distances and coordinates are integers is called an n-cluster (in R^2). We determine the smallest 7-cluster with respect to its diameter. Additionally we provide a toolbox of algorithms which allowed us to computationally locate over 1000 different 7-clusters, some of them having huge integer edge lengths. Along the way, we have exhaustively...

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