TY - GEN
T1 - Unranking combinations using gradient-based optimization
AU - Parque, Victor
AU - Miyashita, Tomoyuki
N1 - Funding Information:
We acknowledge the support from Kakenhi No. 15K18095 to fund this work. Also, we would like to thank Prof. Gautam Dasgupta for the helpful discussions and suggestions.
PY - 2018/12/13
Y1 - 2018/12/13
N2 - Combinations of m out of n are ubiquitous to model a wide class of combinatorial problems. For an ordered sequence of combinations, the unranking function generates the combination associated to an integer number in the ordered sequence. In this paper, we present a new method for unranking combinations by using a gradient-based optimization approach. Exhaustive experiments within computable allowable limits confirmed the feasibility and efficiency of our proposed approach. Particularly, our algorithmic realization aided by a Graphics Processing Unit (GPU) was able to generate arbitrary combinations within 0.571 seconds and 8 iterations in the worst case scenario, for n up to 1000 and m up to 100. Also, the performance and efficiency to generate combinations are independent of n, being meritorious when n is very large compared to m, or when n is time-varying. Furthermore, the number of required iterations to generate the combinations by the gradient-based optimization decreases with m in average, implying the attractive scalability in terms of m. Our proposed approach offers the building blocks to enable the succinct modeling and the efficient optimization of combinatorial structures.
AB - Combinations of m out of n are ubiquitous to model a wide class of combinatorial problems. For an ordered sequence of combinations, the unranking function generates the combination associated to an integer number in the ordered sequence. In this paper, we present a new method for unranking combinations by using a gradient-based optimization approach. Exhaustive experiments within computable allowable limits confirmed the feasibility and efficiency of our proposed approach. Particularly, our algorithmic realization aided by a Graphics Processing Unit (GPU) was able to generate arbitrary combinations within 0.571 seconds and 8 iterations in the worst case scenario, for n up to 1000 and m up to 100. Also, the performance and efficiency to generate combinations are independent of n, being meritorious when n is very large compared to m, or when n is time-varying. Furthermore, the number of required iterations to generate the combinations by the gradient-based optimization decreases with m in average, implying the attractive scalability in terms of m. Our proposed approach offers the building blocks to enable the succinct modeling and the efficient optimization of combinatorial structures.
KW - Binomial
KW - Combinations
KW - Combinatorial
KW - Combinatorics
KW - Gradient based optimization
KW - K out of n
KW - M our of n
KW - Optimization
KW - Representation
KW - Unranking
UR - http://www.scopus.com/inward/record.url?scp=85060821842&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85060821842&partnerID=8YFLogxK
U2 - 10.1109/ICTAI.2018.00094
DO - 10.1109/ICTAI.2018.00094
M3 - Conference contribution
AN - SCOPUS:85060821842
T3 - Proceedings - International Conference on Tools with Artificial Intelligence, ICTAI
SP - 579
EP - 586
BT - Proceedings - 2018 IEEE 30th International Conference on Tools with Artificial Intelligence, ICTAI 2018
PB - IEEE Computer Society
T2 - 30th International Conference on Tools with Artificial Intelligence, ICTAI 2018
Y2 - 5 November 2018 through 7 November 2018
ER -