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CORR
2010
Springer

Balanced Interval Coloring

11 years 11 months ago
Balanced Interval Coloring
We consider the discrepancy problem of coloring n intervals with k colors such that at each point on the line, the maximal difference between the number of intervals of any two colors is minimal. Somewhat surprisingly, a coloring with maximal difference at most one always exists. Furthermore, we give an algorithm with running time O(n log n + kn log k) for its construction. This is in particular interesting because many known results for discrepancy problems are non-constructive. This problem naturally models a load balancing scenario, where n tasks with given start- and endtimes have to be distributed among k servers. Our results imply that this can be done ideally balanced. When generalizing to d-dimensional boxes (instead of intervals), a solution with difference at most one is not always possible. We show that for any d 2 and any k 2 it is NP-complete to decide if such a solution exists, which implies also NP-hardness of the respective minimization problem. In an online scenario...
Antonios Antoniadis, Falk Hüffner, Pascal Len
Added 01 Mar 2011
Updated 01 Mar 2011
Type Journal
Year 2010
Where CORR
Authors Antonios Antoniadis, Falk Hüffner, Pascal Lenzner, Carsten Moldenhauer, Alexander Souza
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