Year: 2024
Type: conference-paper
Abstract: The list-labeling problem captures the basic task of storing a dynamically changing set of up to$n$elements in sorted order in an array of size$m=(1+\Theta(1))n$• The goal is to support insertions and deletions while moving around elements within the array as little as possible. Until recently, the best known upper bound stood at$O(\log^{2}n)$amortized cost. This bound, which was first established in 1981, was finally improved two years ago, when a randomized$O(\log^{3/2}n)$expected-cost algorithm was discovered. The best randomized lower bound for this problem remains$\Omega(\log n)$, and closing this gap is considered to be a major open problem in data structures. In this paper, we present the See-Saw Algorithm, a randomized list-labeling solution that achieves a nearly optimal bound of$O(\log n \text{polyloglog}\ n)$amortized expected cost. This bound is achieved despite at least three lower bounds showing that this type of result is impossible for large classes of solutions.
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: Combinatorial Structures and Processes, G3345895242, G3477743816, RCN: DIMACS/Simons Collaboration on Lower Bounds in Complexity Theory, Collaborative Research: AF: Medium: Adventures in Flatland: Algorithms for Modern Memories, G3800539971, G434337789, Collaborative Research: PPoSS: Planning: Efficient Address Translation with Formal Guarantees for Data-Center-Scale Applications, G4937468798, G5464415299, Collaborative Research: AF: Medium: Adventures in Flatland: Algorithms for Modern Memories, ABR: CSR: Medium: Collaborative Research: FTFS: A Read/Write Optimized Fractal Tree File System, NSF-BSF: Collaborative Research: AF: Small: Algorithmic Performance through History Independence, G7510981485, ABR: CSR: Medium: Collaborative Research: FTFS: A Read/Write Optimized Fractal Tree File System, G8512683158, G9644609
OpenAlex ID: W4404848496