Problem
Research questions and friction points this paper is trying to address.
k-server conjecture
deterministic online algorithm
competitive ratio
metric space
The $k$-server conjecture is true
🤖 AI Summary
证明了k-服务器猜想，使用工作函数算法并通过其代数表示法和矩阵运算进行验证。
📝 Abstract
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 all feasible paths to reach a configuration. In this representation, the minimum and addition operations arising in the definition of optimal costs correspond to addition and multiplication of formal expressions, and each work function value corresponds to the determinant of $k$ columns of the matrix. A request arrival updates the representation via a change of basis and row replacement. The amortized analysis is based on a potential function defined in terms of a larger matrix whose coordinates are pairs of coordinates of the original matrix representation.
Innovation
Methods, ideas, or system contributions that make the work stand out.
work function algorithm
algebraic representation
matrix
determinant
potential function
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