Combinatorial properties of sequences defined by the billiard in paved triangles
Theoretical Computer Science
Balanced sequences and optimal routing
Journal of the ACM (JACM)
Multimodularity, Convexity, and Optimization Properties
Mathematics of Operations Research
Fraenkel's conjecture for six sequences
Discrete Mathematics
Episturmian words and some constructions of de Luca and Rauzy
Theoretical Computer Science
Performance Guarantees in Communication Networks
Performance Guarantees in Communication Networks
ATM Network Performance
Routing Jobs to Servers with Deterministic Service Times
Mathematics of Operations Research
Design and analysis of a class-aware recursive loop scheduler for class-based scheduling
Performance Evaluation
Balance Properties and Distribution of Squares in Circular Words
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
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Consider to construct an infinite sequence, or an infinite word, from a finite set of letters such as each letter is distributed with "good balance," that is, as evenly as possible, when the densities of letters are provided. Such words have been applied to many scheduling and routing problems in various areas. Concerning the balancedness of words, the notions of regularity and balanced words have been exploited. However, it is known that there does not always exist a balanced word for given densities of letters. In this paper, we introduce a new notion called m-balanced words, which gives a measure of "well balancedness" for any words with any densities of letters. We derive some properties of m-balanced words and give a set of algorithms generating well balanced words. We further give a few examples of applications to simple network scheduling problems.