Author

Marek Zbysinski

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Preprint Sep 2026

The $k$-server conjecture is true

The $k$-server conjecture states that a deterministic online algorithm can achieve competitive ratio $k$ on every metric space. We prove the conjecture. Specifically, we show that the work function algorithm satisfies it. Our proof uses a natural algebraic representation of the work function as a matrix, which encodes...

Christian Coester, E. Koutsoupias, Marek Zbysinski · 0 citations

#artificial intelligence Aug 2021

Subgoal Search For Complex Reasoning Tasks

It is shown that a simple approach of generating $k$-th step ahead subgoals is surprisingly efficient on three challenging domains: two popular puzzle games, Sokoban and the Rubik's Cube, and an inequality proving benchmark INT.

K. Czechowski, Tomasz Odrzyg'o'zd'z, Marek Zbysinski et al. · Neural Information Processin... · 41 citations · ⚡3