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Shape-Agnostic Table Overlap Discovery: A Maximum Common Subhypergraph Approach

Ge Lee, Shixun Huang, Zhifeng Bao, Felix Naumann, Shazia Sadiq, Yanchang Zhao

Abstract

Understanding how two tables overlap is useful for many data management tasks, but challenging because tables often differ in row and column orders and lack reliable metadata in practice. Prior work defines the largest rectangular overlap, which identifies the maximal contiguous region of matching cells under row and column permutations. However, real overlaps are rarely rectangular, where many valid matches may lie outside any single contiguous block. In this paper, we introduce the Shape-Agnostic Largest Table Overlap (SALTO), a novel generalized notion of overlap that captures arbitrary-shaped, non-contiguous overlaps between tables. To tackle the combinatorial complexity of row and column permutations, we propose to model each table as a hypergraph, casting SALTO computation into a maximum common subhypergraph problem. We prove their equivalence and show the problem is NP-hard to approximate. To solve it, we propose HyperSplit, a novel branch-and-bound algorithm tailored to table-induced hypergraphs. HyperSplit introduces (i) hypergraph-aware label classes that jointly encode cell values and their row-column memberships to ensure structurally valid correspondences without explicit permutation enumeration, (ii) incidence-guided refinement and upper-bound pruning that leverage row-column connectivity to eliminate infeasible partial matches early, and (iii) a tolerance-based optimization mechanism with a tunable parameter that relaxes pruning by a bounded margin to accelerate convergence, enabling scalable yet accurate overlap discovery. Experiments on real-world datasets show that HyperSplit discovers overlaps more effectively (larger overlaps in up to 78.8% of the cases) and more efficiently than state of the art. Three case studies further demonstrate its practical impact across three tasks: cross-source copy detection, data deduplication, and version comparison.

Shape-Agnostic Table Overlap Discovery: A Maximum Common Subhypergraph Approach

Abstract

Understanding how two tables overlap is useful for many data management tasks, but challenging because tables often differ in row and column orders and lack reliable metadata in practice. Prior work defines the largest rectangular overlap, which identifies the maximal contiguous region of matching cells under row and column permutations. However, real overlaps are rarely rectangular, where many valid matches may lie outside any single contiguous block. In this paper, we introduce the Shape-Agnostic Largest Table Overlap (SALTO), a novel generalized notion of overlap that captures arbitrary-shaped, non-contiguous overlaps between tables. To tackle the combinatorial complexity of row and column permutations, we propose to model each table as a hypergraph, casting SALTO computation into a maximum common subhypergraph problem. We prove their equivalence and show the problem is NP-hard to approximate. To solve it, we propose HyperSplit, a novel branch-and-bound algorithm tailored to table-induced hypergraphs. HyperSplit introduces (i) hypergraph-aware label classes that jointly encode cell values and their row-column memberships to ensure structurally valid correspondences without explicit permutation enumeration, (ii) incidence-guided refinement and upper-bound pruning that leverage row-column connectivity to eliminate infeasible partial matches early, and (iii) a tolerance-based optimization mechanism with a tunable parameter that relaxes pruning by a bounded margin to accelerate convergence, enabling scalable yet accurate overlap discovery. Experiments on real-world datasets show that HyperSplit discovers overlaps more effectively (larger overlaps in up to 78.8% of the cases) and more efficiently than state of the art. Three case studies further demonstrate its practical impact across three tasks: cross-source copy detection, data deduplication, and version comparison.
Paper Structure (34 sections, 4 theorems, 4 equations, 11 figures, 3 tables, 1 algorithm)

This paper contains 34 sections, 4 theorems, 4 equations, 11 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Casting SALTO to Maximum Common Subhypergraph
  4. Table-to-Hypergraph Formulation
  5. Hypergraph
  6. Table-to-Hypergraph Construction
  7. A New Problem: Maximum Common Subhypergraph
  8. Subhypergraph
  9. Common Subhypergraph
  10. Maximum Common Subhypergraph
  11. Establishing Problem Equivalence
  12. Hardness Analysis
  13. HyperSplit: Solving Maximum Common Subhypergraph
  14. Background: McSplit and Its Limitations
  15. Overview of HyperSplit
  16. ...and 19 more sections

Key Result

Theorem 1

Let $T$ be a table and $H(T)$ be its associated hypergraph. For any table $T'$ obtained by permuting the rows and/or columns of $T$, the hypergraphs $H(T)$ and $H(T')$ are isomorphic. Consequently, structural properties of the hypergraph representation are preserved under such permutations.

Figures (11)

  • Figure 1: Comparison between Sloth's largest rectangular overlap and our largest shape-agnostic overlap
  • Figure 2: Hypergraph representation of Tables X and Y and their maximum common subhypergraph. Cell values shared by both tables are shown in bold. Hyperedges are visualized as convex hulls (purple for rows, green for columns) enclosing their associated nodes.
  • Figure 3: Distributions of table sizes (log-scale)
  • Figure 4: Distributions of node counts, row-hyperedge counts and column-hyperedge counts (log-scale)
  • Figure 5: Overlap ratio comparison of HyperSplit against Sloth, GPT-4.1 and CR-Jaccard
  • ...and 6 more figures

Theorems & Definitions (17)

  • Example 1
  • Definition 1: Table
  • Definition 2: Row and Column Permutations
  • Definition 3: Table Overlap
  • Definition 4: Shape-Agnostic Largest Table Overlap
  • Definition 5: Hypergraph
  • Example 2
  • Example 3
  • Definition 6: Subhypergraph
  • Example 4
  • ...and 7 more