TY - GEN
T1 - On approximating minimum infrequent and maximum frequent sets
AU - Boley, Mario
PY - 2007
Y1 - 2007
N2 - The maximum cardinality of a frequent set as well as the minimum cardinality of an infrequent set are important characteristic numbers in frequent (item) set mining. Gunopulos et al. [10] have shown that finding a maximum frequent set is NP-hard. In this paper I show that the minimization problem is also NP-hard. As a next step I investigate whether these problems can be approximated. While a simple greedy algorithm turns out to approximate a minimum infrequent set within a logarithmic factor one can show that there is no such algorithm for the maximization problem.
AB - The maximum cardinality of a frequent set as well as the minimum cardinality of an infrequent set are important characteristic numbers in frequent (item) set mining. Gunopulos et al. [10] have shown that finding a maximum frequent set is NP-hard. In this paper I show that the minimization problem is also NP-hard. As a next step I investigate whether these problems can be approximated. While a simple greedy algorithm turns out to approximate a minimum infrequent set within a logarithmic factor one can show that there is no such algorithm for the maximization problem.
UR - http://www.scopus.com/inward/record.url?scp=38149017160&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-75488-6_8
DO - 10.1007/978-3-540-75488-6_8
M3 - Conference contribution
AN - SCOPUS:38149017160
SN - 9783540754879
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 68
EP - 77
BT - Discovery Science - 10th International Conference, DS 2007, Proceedings
PB - Springer Verlag
T2 - 10th International Conference on Discovery Science, DS 2007
Y2 - 1 October 2007 through 4 October 2007
ER -