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Cabello S.,IMFM | Cabello S.,University of Ljubljana | Cheong O.,KAIST | Knauer C.,University of Bayreuth | Schlipf L.,Free University of Berlin
Computational Geometry: Theory and Applications | Year: 2015

We consider the following geometric optimization problem: find a maximum-area rectangle and a maximum-perimeter rectangle contained in a given convex polygon with n vertices. We give exact algorithms that solve these problems in time O(n3). We also give (1-ε)-approximation algorithms that take time O(ε-1/2log n+ε-3/2). © 2015 Elsevier B.V. Source

Zerovnik J.,University of Ljubljana | Kuzma B.,IMFM | Kuzma B.,University of Primorska
Proceedings of the 11th International Symposium on Operational Research in Slovenia, SOR 2011 | Year: 2011

Densities of ball packing with two different sizes of balls is studied. For several ratios between the radii estimates for densities on unbounded regions are given. Source

Kozak J.,University of Ljubljana | Krajnc M.,University of Ljubljana | Vitrih V.,IMFM | Vitrih V.,University of Primorska
Computer Aided Geometric Design | Year: 2016

In this paper a new approach for a construction of polynomial surfaces with rational field of unit normals (PN surfaces) is presented. It is based on bivariate polynomials with quaternion coefficients. Relations between these coefficients are derived that allow one to construct PN surfaces of general odd and even degrees. For low degree PN surfaces the theoretical results are supplemented with algorithms and illustrated with numerical examples. © 2016 Elsevier B.V. Source

Dolinar G.,University of Ljubljana | Guterman A.E.,Moscow State University | Kuzma B.,University of Primorska | Orel M.,IMFM
European Journal of Combinatorics | Year: 2011

Let F be a finite field of characteristic different from 2. We show that no bijective map transforms the permanent into the determinant when the cardinality of F is sufficiently large. We also give an example of a non-bijective map when F is arbitrary and an example of a bijective map when F is infinite which do transform the permanent into the determinant. The technique developed allows us to estimate the probability of the permanent and the determinant of matrices over finite fields having a given value. Our results are also true over finite rings without zero divisors. © 2010 Elsevier Ltd. Source

Cabello S.,IMFM | Cabello S.,University of Ljubljana | Jejcic M.,University of Ljubljana
Computational Geometry: Theory and Applications | Year: 2015

Let G be a unit disk graph in the plane defined by n disks whose positions are known. For the case when G is unweighted, we give a simple algorithm to compute a shortest path tree from a given source in O(nlog n) time. For the case when G is weighted, we show that a shortest path tree from a given source can be computed in O(n1+ε) time, improving the previous best time bound of O(n4/3+ε). © 2014 Published by Elsevier B.V. Source

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