TY - GEN
T1 - The Impact of Negation on the Complexity of the Shapley Value in Conjunctive Queries
AU - Reshef, Alon
AU - Kimelfeld, Benny
AU - Livshits, Ester
N1 - Publisher Copyright:
© 2020 Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems. All rights reserved.
PY - 2020/6/14
Y1 - 2020/6/14
N2 - The Shapley value is a conventional and well-studied function for determining the contribution of a player to the coalition in a cooperative game. Among its applications in a plethora of domains, it has recently been proposed to use the Shapley value for quantifying the contribution of a tuple to the result of a database query. In particular, we have a thorough understanding of the tractability frontier for the class of Conjunctive Queries (CQs) and aggregate functions over CQs. It has also been established that a tractable (randomized) multiplicative approximation exists for every union of CQs. Nevertheless, all of these results are based on the monotonicity of CQs. In this work, we investigate the implication of negation on the complexity of Shapley computation, in both the exact and approximate senses. We generalize a known dichotomy to account for negated atoms. We also show that negation fundamentally changes the complexity of approximation. We do so by drawing a connection to the problem of deciding whether a tuple is "relevant" to a query, and by analyzing its complexity.
AB - The Shapley value is a conventional and well-studied function for determining the contribution of a player to the coalition in a cooperative game. Among its applications in a plethora of domains, it has recently been proposed to use the Shapley value for quantifying the contribution of a tuple to the result of a database query. In particular, we have a thorough understanding of the tractability frontier for the class of Conjunctive Queries (CQs) and aggregate functions over CQs. It has also been established that a tractable (randomized) multiplicative approximation exists for every union of CQs. Nevertheless, all of these results are based on the monotonicity of CQs. In this work, we investigate the implication of negation on the complexity of Shapley computation, in both the exact and approximate senses. We generalize a known dichotomy to account for negated atoms. We also show that negation fundamentally changes the complexity of approximation. We do so by drawing a connection to the problem of deciding whether a tuple is "relevant" to a query, and by analyzing its complexity.
KW - conjunctive queries
KW - query answering
KW - shapley value
UR - http://www.scopus.com/inward/record.url?scp=85086235803&partnerID=8YFLogxK
U2 - 10.1145/3375395.3387664
DO - 10.1145/3375395.3387664
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???
AN - SCOPUS:85086235803
T3 - Proceedings of the 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems
SP - 285
EP - 297
BT - PODS 2020 - Proceedings of the 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems
T2 - 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2020
Y2 - 14 June 2020 through 19 June 2020
ER -