An integer linear program (ILP) is symmetric if its variables can be permuted without
changing the structure of the problem. Areas where symmetric ILPs arise range from applied …

CLASSIFICATION OF EIGHT-DIMENSIONAL PERFECT FORMS 1. Introduction A lattice L is a
rank d subgroup of Rd. It is of the form L = Page 1 ELECTRONIC RESEARCH …

We give a short survey on computational techniques which can be used to solve the
representation conversion problem for polyhedra up to symmetries. We in particular discuss …

We address the problem of designing a network built on several layers. This problem occurs
in practical applications but has not been studied extensively from the point of view of global …

This book introduces oriented version of metrics and cuts and their multidimensional
analogues, as well as partial metrics and weighted metrics. It is a follow-up of Geometry of …

A semi-metric is defined as a function (x, y)↦→ d (x, y) satisfying d (x, x)= 0, d (x, y)= d (y, x)
and the triangle inequality d (x, z)≤ d (x, y)+ d (y, z). The set of all semi-metrics on n points …

Given a graph G, a K_3-decomposition of G, also called a triangle decomposition, is a set of
subgraphs isomorphic to K_3 whose edges partition the edge set of G. Further, a rational …

SYNOPTIC ABSTRACT We consider polyhedral convex cones, associated with quasi-semi-
metrics (oriented distances), in particular, with oriented multi-cuts, on n points. We computed …

The double description method is a simple but widely used algorithm for computation of
extreme points in polyhedral sets. One key aspect of its implementation is the question of …

The lattice packing problem in dimension 9 is a long-standing open problem. We consider a
classical algorithm by Voronoi to solve the lattice packing problem in any dimension, by …