On the binary expansion of irrational algebraic numbers
On the hardness of approximating some NP-optimization problems related to minimum linear ordering problem
We study hardness of approximating several minimaximal and maximinimal NP-optimization problems related to the minimum linear ordering problem (MINLOP). MINLOP is to find a minimum weight acyclic tournament in a given arc-weighted complete digraph. MINLOP is APX-hard but its unweighted version is polynomial time solvable. We prove that MIN-MAX-SUBDAG problem, which is a generalization of MINLOP and requires to find a minimum cardinality maximal acyclic subdigraph of a given digraph, is, however,...
On the Hardness of Approximating Some NP-optimization Problems Related to Minimum Linear Ordering Problem
We study hardness of approximating several minimaximal and maximinimal NP-optimization problems related to the minimum linear ordering problem (MINLOP). MINLOP is to find a minimum weight acyclic tournament in a given arc-weighted complete digraph. MINLOP is APX-hard but its unweighted version is polynomial time solvable. We prove that MIN-MAX-SUBDAG problem, which is a generalization of MINLOP and requires to find a minimum cardinality maximal acyclic subdigraph of a given digraph, is, however,...
On the number of binary signed digit representations of a given weight
Binary signed digit representations (BSDR’s) of integers have been studied since the 1950’s. Their study was originally motivated by multiplication and division algorithms for integers and later by arithmetics on elliptic curves. Our paper is motivated by differential cryptanalysis of hash functions. We give an upper bound for the number of BSDR’s of a given weight. Our result improves the upper bound on the number of BSDR’s with minimal weight stated by Grabner and Heuberger in On the number of...