TY  - JOUR
A1  - Möller, Bernhard
T1  - Towards antichain algebra
T2  - Lecture Notes in Computer Science
N2  - We use an algebra of preference strict-orders to give a formal derivation of the standard Block-Nested Loop (BNL) algorithm for computing the best or maximal objects w.r.t. such an order. This derivation is presented in terms of antichains, i.e., sets of mutually incomparable objects. We define an approximation relation between antichains that reflects the steps taken by the BNL algorithm. This induces a semilattice and the operator computing the maximal objects of a subset can be viewed as a closure operator in an associated pre-ordered set and hence yields a characterisation of antichains in terms of a Galois connection.
Y1  - 2015
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/58734
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-587347
SN  - 9783319247038
SN  - 9783319247045
SN  - 0302-9743
SN  - 1611-3349
VL  - 9348
SP  - 344
EP  - 361
PB  - Springer International
CY  - Cham
ER  -