Continuous $k$-Regret Minimization Queries: A Dynamic Coreset Approach

Finding a small set of representative tuples from a large database is an important functionality for supporting multi-criteria decision making. Top-
$k$
queries and skyline queries are two widely studied queries to fulfill this task. However, both of them have some limitations: a top-
$k$
query requires the user to provide her utility functions for finding the
$k$
tuples with the highest scores as the result; a skyline query does not need any user-specified utility function but cannot control the result size. To overcome their drawbacks, the
$k$
-regret minimization query was proposed and received much attention recently, since it does not require any user-specified utility function and returns a fixed-size result set. Specifically, it selects a set
$R$
of tuples with a pre-defined size
$r$
from a database
$D$
such that the
maximum $k$-regret ratio
, which captures how well the top-ranked tuple in
$R$
represents the top-
$k$
tuples in
$D$
for any possible utility function, is minimized. Although there have been many methods for
$k$
-regret minimization query processing, most of them are designed for static databases without tuple insertions and deletions. The only known algorithm to process continuous
$k$
-regret minimization queries (C
$k$
RMQ) in dynamic databases suffers from suboptimal approximation and high time complexity. In this paper, we propose a novel dynamic coreset-based approach, called
DynCore
, for C
$k$
RMQ processing. It achieves the same (asymptotically optimal) upper bound on the maximum
$k$
-regret ratio as the best-known static algorithm. Meanwhile, its time complexity is sublinear to the database size, which is significantly lower than that of the existing dynamic algorithm. The efficiency and effectiveness of
DynCore
is confirmed by experimental results on real-world and synthetic datasets.