On the Decidability of Semi-Linearity for Semi-Algebraic Sets and its Implications for Spatial Databases (extended abstract)
Summary: Proves decidability of whether a semi-algebraic set is semi-linear, highlights the role of coefficient types and the geometric notion of regularity, and shows regular points are computable in FO+linear. Consequence: yields a syntactic language exactly capturing the FO+poly queries that are linear, circumventing previous undecidability of testing linearity. (summarized by gpt-5-mini on Feb 09 2026)
Incoming Non-self Citations Over Time
Authors
- 1. Freddy Dumortier (University of Limburg)
- 2. Marc Gyssens (University of Limburg)
- 3. Luc Vandeurzen (University of Limburg)
- 4. Dirk Van Gucht (Indiana University)
BibTeX Citation
@inproceedings{dumortier_pods97,
address = {New York, NY, USA},
series = {{PODS} '97},
title = {{On the Decidability of Semi-Linearity for Semi-Algebraic Sets and its Implications for Spatial Databases (extended abstract)}},
url = {https://dl.acm.org/doi/10.1145/263661.263670},
doi = {10.1145/263661.263670},
booktitle = {Proceedings of the {ACM} {SIGMOD} Symposium on {Principles} of {Database} {Systems}},
publisher = {Association for Computing Machinery},
author = {Dumortier, Freddy and Gyssens, Marc and Vandeurzen, Luc and Van Gucht, Dirk},
year = {1997}
}
Incoming Citations (Sorted by Pagerank)
Showing 6 of 6 citing papers.
| Rank | Citing Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 1,561 | Efficient Searching with Linear Constraints (Extended Abstract) | 1998 | PODS | 0.00010361147 |
| 3,043 | The DEDALE System for Complex Spatial Queries | 1998 | SIGMOD | 7.8228924e-05 |
| 4,203 | An Expressive Language for Linear Spatial Database Queries (extended abstract) | 1998 | PODS | 6.8354052e-05 |
| 4,226 | Safe Constraint Queries | 1998 | PODS | 6.8211482e-05 |
| 12,875 | Fixed-Point Query Languages for Linear Constraint Databases | 2000 | PODS | 5.093636e-05 |
| 12,876 | Linear approximation of planar spatial databases using transitive-closure logic | 2000 | PODS | 5.093636e-05 |
Previous
Page 1 / 1
Next
Outgoing Citations (Sorted by Pagerank)
Showing 4 of 4 cited papers.
Citations counted here include only citations to other VLDB/SIGMOD/CIDR/PODS papers in this database.
| Rank | Cited Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 889 | Constraint Programming and Database Languages: A Tutorial | 1995 | PODS | 0.00013398105 |
| 1,473 | Towards a Theory of Spatial Database Queries (Extended Abstract) | 1994 | PODS | 0.0001066845 |
| 1,890 | Relational Expressive Power of Constraint Query Languages | 1996 | PODS | 9.5330753e-05 |
| 3,591 | The LyriC Language: Querying Constraint Objects | 1995 | SIGMOD | 7.279053e-05 |
Previous
Page 1 / 1
Next
Semantically Similar Papers
| # | Overall Rank | Paper | Year | Venue |
|---|---|---|---|---|
| 1 | 5,523 | Dense-Order Constraint Databases (Extended Abstract) | 1995 | PODS |
| 2 | 633 | The Complexity of Querying Indefinite Data about Linearly Ordered Domains (Preliminary Version) | 1992 | PODS |
| 3 | 8,528 | Aggregate Queries on Sparse Databases | 2020 | PODS |
| 4 | 12,763 | A characterization of first-order topological properties of planar spatial data (Extended abstract) | 2004 | PODS |
| 5 | 1,473 | Towards a Theory of Spatial Database Queries (Extended Abstract) | 1994 | PODS |
| 6 | 12,875 | Fixed-Point Query Languages for Linear Constraint Databases | 2000 | PODS |
| 7 | 3,695 | Topological Queries in Spatial Databases | 1996 | PODS |
| 8 | 8,052 | Complete geometrical query languages (extended abstract) | 1997 | PODS |
| 9 | 4,203 | An Expressive Language for Linear Spatial Database Queries (extended abstract) | 1998 | PODS |
| 10 | 12,876 | Linear approximation of planar spatial databases using transitive-closure logic | 2000 | PODS |