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Improved Interactive Protocol for Synchronizing From Deletions

Haolun, Ni, Lev Tauz, Ryan Gabrys, Lara Dolecek

TL;DR

This work advances data synchronization under deletions by embedding multi-deletion correction codes into a baseline interactive protocol and introducing adaptive segmenting. The proposed three-module scheme—Matching, Deletion Recovery, and Error Correction—leverages segment-length tuning and generalized upper bounds to lower communication cost while maintaining polynomial-time feasibility. The authors provide a rigorous upper bound on transmitted bits and validate improvements experimentally, showing notable reductions in redundancy compared to the baseline. The approach enables low-redundancy synchronization in environments with deletions, with potential extensions to broader edit models and more efficient multi-deletion codes.

Abstract

Data synchronization is a fundamental problem with applications in diverse fields such as cloud storage, genomics, and distributed systems. This paper addresses the challenge of synchronizing two files, one of which is a subsequence of the other and related through a constant rate of deletions, using an improved communication protocol. Building upon prior work, we integrate advanced multi-deletion correction codes into an existing baseline protocol, which previously relied on single-deletion correction. Our proposed protocol reduces communication cost by leveraging more general partitioning techniques as well as multi-deletion error correction. We derive a generalized upper bound on the expected number of transmitted bits, applicable to a broad class of deletion correction codes. Experimental results demonstrate that our approach outperforms the baseline in communication cost. These findings establish the efficacy of the improved protocol in achieving low-redundancy synchronization in scenarios where deletion errors occur.

Improved Interactive Protocol for Synchronizing From Deletions

TL;DR

This work advances data synchronization under deletions by embedding multi-deletion correction codes into a baseline interactive protocol and introducing adaptive segmenting. The proposed three-module scheme—Matching, Deletion Recovery, and Error Correction—leverages segment-length tuning and generalized upper bounds to lower communication cost while maintaining polynomial-time feasibility. The authors provide a rigorous upper bound on transmitted bits and validate improvements experimentally, showing notable reductions in redundancy compared to the baseline. The approach enables low-redundancy synchronization in environments with deletions, with potential extensions to broader edit models and more efficient multi-deletion codes.

Abstract

Data synchronization is a fundamental problem with applications in diverse fields such as cloud storage, genomics, and distributed systems. This paper addresses the challenge of synchronizing two files, one of which is a subsequence of the other and related through a constant rate of deletions, using an improved communication protocol. Building upon prior work, we integrate advanced multi-deletion correction codes into an existing baseline protocol, which previously relied on single-deletion correction. Our proposed protocol reduces communication cost by leveraging more general partitioning techniques as well as multi-deletion error correction. We derive a generalized upper bound on the expected number of transmitted bits, applicable to a broad class of deletion correction codes. Experimental results demonstrate that our approach outperforms the baseline in communication cost. These findings establish the efficacy of the improved protocol in achieving low-redundancy synchronization in scenarios where deletion errors occur.

Paper Structure

This paper contains 17 sections, 15 theorems, 60 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Improved Synchronization Algorithm
  4. The Matching Module
  5. The Deletion Recovery Module
  6. The Error Correction Module
  7. Analysis and Discussion
  8. Experimental Results
  9. Effect of Segment Length
  10. Comparison with the Baseline Protocol
  11. Proof of Theorem \ref{['theorem:improved']}
  12. Number of Bits Transmitted in Modules I
  13. Number of Bits Transmitted in Module II
  14. Number of Bits Transmitted in a Single Section of Module II
  15. Total Number of Bits Transmitted in Module II
  16. ...and 2 more sections

Key Result

Theorem 1

Let $s > 0$ be the segment length multiplier. Let $c>0$ be the delimiter length coefficient in the Deletion Recovery Module. Let $w$ be the maximum number of deletions that we can correct with a set of multi-deletion correction codes. Let $a_i \geq 1, i \in [1, \dots, w]$, be the efficiency of the $

Figures (3)

  • Figure 1: Graph of the redundancy coefficient $r$ as a function of $s$ for various values of $w$ with fixed parameters $a = 1$ and $c = 3$.
  • Figure 2: Number of bits transmitted for both the baseline and improved protocols across varying segment length coefficients, where the segment length is scaled by the coefficient. Each subfigure represents a different deletion rate.
  • Figure 3: Number of bits transmitted for the baseline and improved protocols at different deletion rates, with sequence length $n=50,000$ and segment length $L_S = \frac{2}{\beta}$.

Theorems & Definitions (18)

  • Theorem 1
  • Theorem 2: from Lemma 1, ori
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Lemma 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • ...and 8 more