We revisit the problem max-min degree arborescence, which was introduced by Bateni et al. [STOC'09] as a central special case of the general Santa Claus problem, which constitutes a notorious open question in approximation algorithms. In the former problem ...
Knapsack and Subset Sum are fundamental NP-hard problems in combinatorial optimization. Recently there has been a growing interest in understanding the best possible pseudopolynomial running times for these problems with respect to various parameters. In t ...
Schloss Dagstuhl -- Leibniz-Zentrum für Informatik2021
The RESTRICTED ASSIGNMENT problem is a prominent special case of SCHEDULING ON UNRELATED PARALLEL MACHINES. For the strongest known linear programming relaxation, the configuration LP, we improve the nonconstructive bound on its integrality gap from 1.9412 ...
We consider the problem of finding a basis of a matroid with weight exactly equal to a given target. Here weights can be discrete values from {−Δ,…,Δ} or more generally m-dimensional vectors of such discrete values. We resolve the para ...
We relate discrepancy theory with the classic scheduling problems of minimizing max flow time and total flow time on unrelated machines. Specifically, we give a general reduction that allows us to transfer discrepancy bounds in the prefix Beck-Fiala (bound ...
Weighted flow time is a fundamental and very well-studied objective function in scheduling. In this paper, we study the setting of a single machine with preemptions. ...
In the restricted Santa Claus problem we are given resources R and players P. Every resource j is an element of R. has a value v(j) and every player i is an element of P desires a set of resources R(i). We are interested in distributing the resources to pl ...
