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Improved Explicit Data Structures in the Bit-Probe Model Using Error-Correcting Codes

Speaker: Santhoshini
Title: Improved Explicit Data Structures in the Bit-Probe Model Using Error-Correcting Codes
Date: 01 Oct 2020 17:45-19:00 EST (talk starts at 18:00)
Location: Zoom
Food: Self-prepared

Abstract: We consider the bit-probe complexity of the set membership problem: represent an n-element subset S of an m-element universe as a succinct bit vector so that membership queries of the form “Is $x \in S$” can be answered using at most t probes into the bit vector. Let $s(m,n,t)$ denote the minimum number of bits of storage needed when the probes are adaptive. Buhrman, Miltersen, Radhakrishnan, and Venkatesh proved that $s(m,n,t)\gtrsim m^{1/t}$ [STOC 2000]. In this work, we construct explicit adaptive data structures which show that $s(m,n,t) \lesssim m^{1/(t-n/2^{t/n})}$ for $t \ge n \log n$ This matches the previous non-explicit upper bound proved by Radhakrishnan, Shah, and Shanigrahi (ESA 2010). The key ingredient in our work is a clever use of error-correcting codes to encode information in the query paths in the adaptive data structure tree in order to optimize space and query-time.

This is a joint-work with Palash Dey and Jaikumar Radhakrishnan that was published in MFCS’20. Link to the paper Link to the short talk (in case you can’t make it to the TGINF :))

I will try not to assume any prior knowledge of data structures or error-correcting codes.