Lower Bounds for Predecessor Searching in the Cell Probe Model

Title: Lower Bounds for Predecessor Searching in the Cell Probe Model

Abstract: This research article explores the problem of static predecessor searching in the cell probe model, a widely used model for studying data structures. The authors present a new lower bound proof for this problem, which is more efficient and simpler than previous methods. This proof works for both deterministic and randomized query schemes, and it uses a technique called round elimination. The authors also provide a strong round elimination lemma that allows them to obtain tight lower bounds for the predecessor problem. Additionally, they show how this lemma can be used to improve round elimination tradeoffs for other problems.

Main Research Question: How can we design efficient and simple methods for answering predecessor queries in the cell probe model?

Methodology: The authors use the round elimination approach, which involves eliminating rounds of communication between the query scheme and the storage scheme. This technique is used to prove a new lower bound for the number of probes needed to answer predecessor queries.

Results: The authors present a new lower bound proof for static predecessor searching in the cell probe model. This proof is more efficient and simpler than previous methods, and it works for both deterministic and randomized query schemes. They also provide a strong round elimination lemma that allows them to obtain tight lower bounds for the predecessor problem.

Implications: The new lower bound proof and round elimination lemma presented in this article have several implications. First, they provide a more efficient and simpler method for answering predecessor queries in the cell probe model. Second, they show that the round elimination approach can be used to obtain tight lower bounds for the predecessor problem. Finally, they demonstrate how the round elimination lemma can be used to improve round elimination tradeoffs for other problems.

Link to Article: https://arxiv.org/abs/0309033v1 Authors: arXiv ID: 0309033v1