TY - GEN
T1 - The Complexity of the Shapley Value for Regular Path Queries
AU - Khalil, Majd
AU - Kimelfeld, Benny
N1 - Publisher Copyright: © Majd Khalil and Benny Kimelfeld; licensed under Creative Commons License CC-BY 4.0 26th International Conference on Database Theory (ICDT 2023)
PY - 2023/3/1
Y1 - 2023/3/1
N2 - A path query extracts vertex tuples from a labeled graph, based on the words that are formed by the paths connecting the vertices. We study the computational complexity of measuring the contribution of edges and vertices to an answer to a path query, focusing on the class of conjunctive regular path queries. To measure this contribution, we adopt the traditional Shapley value from cooperative game theory. This value has been recently proposed and studied in the context of relational database queries and has uses in a plethora of other domains. We first study the contribution of edges and show that the exact Shapley value is almost always hard to compute. Specifically, it is #P-hard to calculate the contribution of an edge whenever at least one (non-redundant) conjunct allows for a word of length three or more. In the case of regular path queries (i.e., no conjunction), the problem is tractable if the query has only words of length at most two; hence, this property fully characterizes the tractability of the problem. On the other hand, if we allow for an approximation error, then it is straightforward to obtain an efficient scheme (FPRAS) for an additive approximation. Yet, a multiplicative approximation is harder to obtain. We establish that in the case of conjunctive regular path queries, a multiplicative approximation of the Shapley value of an edge can be computed in polynomial time if and only if all query atoms are finite languages (assuming non-redundancy and conventional complexity limitations). We also study the analogous situation where we wish to determine the contribution of a vertex, rather than an edge, and establish complexity results of similar nature.
AB - A path query extracts vertex tuples from a labeled graph, based on the words that are formed by the paths connecting the vertices. We study the computational complexity of measuring the contribution of edges and vertices to an answer to a path query, focusing on the class of conjunctive regular path queries. To measure this contribution, we adopt the traditional Shapley value from cooperative game theory. This value has been recently proposed and studied in the context of relational database queries and has uses in a plethora of other domains. We first study the contribution of edges and show that the exact Shapley value is almost always hard to compute. Specifically, it is #P-hard to calculate the contribution of an edge whenever at least one (non-redundant) conjunct allows for a word of length three or more. In the case of regular path queries (i.e., no conjunction), the problem is tractable if the query has only words of length at most two; hence, this property fully characterizes the tractability of the problem. On the other hand, if we allow for an approximation error, then it is straightforward to obtain an efficient scheme (FPRAS) for an additive approximation. Yet, a multiplicative approximation is harder to obtain. We establish that in the case of conjunctive regular path queries, a multiplicative approximation of the Shapley value of an edge can be computed in polynomial time if and only if all query atoms are finite languages (assuming non-redundancy and conventional complexity limitations). We also study the analogous situation where we wish to determine the contribution of a vertex, rather than an edge, and establish complexity results of similar nature.
KW - Path queries
KW - Shapley value
KW - graph databases
KW - regular path queries
UR - http://www.scopus.com/inward/record.url?scp=85150725949&partnerID=8YFLogxK
U2 - https://doi.org/10.4230/LIPIcs.ICDT.2023.11
DO - https://doi.org/10.4230/LIPIcs.ICDT.2023.11
M3 - منشور من مؤتمر
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 26th International Conference on Database Theory, ICDT 2023
A2 - Geerts, Floris
A2 - Vandevoort, Brecht
T2 - 26th International Conference on Database Theory, ICDT 2023
Y2 - 28 March 2023 through 31 March 2023
ER -