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arXiv · 2501.06246

A Partition Cover Approach to Tokenization

Jia Peng Lim·Shawn Tan·Davin Choo·Hady W. Lauw
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Abstract

Tokenization is the process of encoding strings into tokens of a fixed vocabulary size, and is widely utilized in Natural Language Processing applications. The leading tokenization algorithm today is Byte-Pair Encoding (BPE), which formulates the tokenization problem as a compression problem and tackles it by performing sequences of merges. In this work, we formulate tokenization as an optimization objective, show that it is NP-hard via a simple reduction from vertex cover, and propose a polynomial-time greedy algorithm GreedTok. Our formulation naturally relaxes to the well-studied weighted maximum coverage problem which has a simple $(1 - 1/e)$-approximation algorithm GreedWMC. Through empirical evaluations on real-world corpora, we show that GreedTok outperforms BPE and Unigram on compression and achieves a covering score comparable to GreedWMC. Finally, our extensive pre-training for two transformer-based language models with 1 billion parameters, comparing the choices of BPE and GreedTok as the tokenizer, shows that GreedTok achieves a lower bit per byte even when we control for either the total dataset proportion or total training tokens.

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Jia Peng Lim, Shawn Tan, Davin Choo, Hady W. Lauw. 2025-09-28. A Partition Cover Approach to Tokenization. https://arxiv.org/abs/2501.06246

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