TY - GEN

T1 - Quantifying the Loss of Acyclic Join Dependencies

AU - Kenig, Batya

AU - Weinberger, Nir

N1 - Publisher Copyright:
© 2023 ACM.

PY - 2023/6/18

Y1 - 2023/6/18

N2 - Acyclic schemes posses known benefits for database design, speeding up queries, and reducing space requirements. An acyclic join dependency (AJD) is lossless with respect to a universal relation if joining the projections associated with the schema results in the original universal relation. An intuitive and standard measure of loss entailed by an AJD is the number of redundant tuples generated by the acyclic join. Recent work has shown that the loss of an AJD can also be characterized by an information-Theoretic measure. Motivated by the problem of automatically fitting an acyclic schema to a universal relation, we investigate the connection between these two characterizations of loss. We first show that the loss of an AJD is captured using the notion of KL-Divergence. We then show that the KL-divergence can be used to bound the number of redundant tuples. We prove a deterministic lower bound on the percentage of redundant tuples. For an upper bound, we propose a random database model, and establish a high probability bound on the percentage of redundant tuples, which coincides with the lower bound for large databases.

AB - Acyclic schemes posses known benefits for database design, speeding up queries, and reducing space requirements. An acyclic join dependency (AJD) is lossless with respect to a universal relation if joining the projections associated with the schema results in the original universal relation. An intuitive and standard measure of loss entailed by an AJD is the number of redundant tuples generated by the acyclic join. Recent work has shown that the loss of an AJD can also be characterized by an information-Theoretic measure. Motivated by the problem of automatically fitting an acyclic schema to a universal relation, we investigate the connection between these two characterizations of loss. We first show that the loss of an AJD is captured using the notion of KL-Divergence. We then show that the KL-divergence can be used to bound the number of redundant tuples. We prove a deterministic lower bound on the percentage of redundant tuples. For an upper bound, we propose a random database model, and establish a high probability bound on the percentage of redundant tuples, which coincides with the lower bound for large databases.

KW - acyclic schemas

KW - decomposition

KW - normalization

KW - universal relation

UR - http://www.scopus.com/inward/record.url?scp=85164259846&partnerID=8YFLogxK

U2 - 10.1145/3584372.3588658

DO - 10.1145/3584372.3588658

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AN - SCOPUS:85164259846

T3 - Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems

SP - 329

EP - 338

BT - PODS 2023 - Proceedings of the 42nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

PB - Association for Computing Machinery

T2 - 42nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2023

Y2 - 18 June 2023 through 23 June 2023

ER -