TY - GEN
T1 - Solving the Identifying Code Set Problem with Grouped Independent Support
AU - Latour, Anna L.D.
AU - Sen, Arunabha
AU - Meel, Kuldeep S.
N1 - Publisher Copyright:
© 2023 International Joint Conferences on Artificial Intelligence. All rights reserved.
PY - 2023
Y1 - 2023
N2 - An important problem in network science is finding an optimal placement of sensors in nodes in order to uniquely detect failures in the network. This problem can be modelled as an identifying code set (ICS) problem, introduced by Karpovsky et al. in 1998. The ICS problem aims to find a cover of a set S, such that the elements in the cover define a unique signature for each of the elements of S, and to minimise the cover's cardinality. In this work, we study a generalised identifying code set (GICS) problem, where a unique signature must be found for each subset of S that has a cardinality of at most k (instead of just each element of S). The concept of an independent support of a Boolean formula was introduced by Chakraborty et al. in 2014 to speed up propositional model counting, by identifying a subset of variables whose truth assignments uniquely define those of the other variables. In this work, we introduce an extended version of independent support, grouped independent support (GIS), and show how to reduce the GICS problem to the GIS problem. We then propose a new solving method for finding a GICS, based on finding a GIS. We show that the prior state-of-the-art approaches yield integer-linear programming (ILP) models whose sizes grow exponentially with the problem size and k, while our GIS encoding only grows polynomially with the problem size and k. While the ILP approach can solve the GICS problem on networks of at most 494 nodes, the GIS-based method can handle networks of up to 21 363 nodes; a ∼ 40× improvement. The GIS-based method shows up to a 520× improvement on the ILP-based method in terms of median solving time. For the majority of the instances that can be encoded and solved by both methods, the cardinality of the solution returned by the GIS-based method is less than 10% larger than the cardinality of the solution found by the ILP method.
AB - An important problem in network science is finding an optimal placement of sensors in nodes in order to uniquely detect failures in the network. This problem can be modelled as an identifying code set (ICS) problem, introduced by Karpovsky et al. in 1998. The ICS problem aims to find a cover of a set S, such that the elements in the cover define a unique signature for each of the elements of S, and to minimise the cover's cardinality. In this work, we study a generalised identifying code set (GICS) problem, where a unique signature must be found for each subset of S that has a cardinality of at most k (instead of just each element of S). The concept of an independent support of a Boolean formula was introduced by Chakraborty et al. in 2014 to speed up propositional model counting, by identifying a subset of variables whose truth assignments uniquely define those of the other variables. In this work, we introduce an extended version of independent support, grouped independent support (GIS), and show how to reduce the GICS problem to the GIS problem. We then propose a new solving method for finding a GICS, based on finding a GIS. We show that the prior state-of-the-art approaches yield integer-linear programming (ILP) models whose sizes grow exponentially with the problem size and k, while our GIS encoding only grows polynomially with the problem size and k. While the ILP approach can solve the GICS problem on networks of at most 494 nodes, the GIS-based method can handle networks of up to 21 363 nodes; a ∼ 40× improvement. The GIS-based method shows up to a 520× improvement on the ILP-based method in terms of median solving time. For the majority of the instances that can be encoded and solved by both methods, the cardinality of the solution returned by the GIS-based method is less than 10% larger than the cardinality of the solution found by the ILP method.
UR - http://www.scopus.com/inward/record.url?scp=85170365066&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85170365066&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:85170365066
T3 - IJCAI International Joint Conference on Artificial Intelligence
SP - 1971
EP - 1978
BT - Proceedings of the 32nd International Joint Conference on Artificial Intelligence, IJCAI 2023
A2 - Elkind, Edith
PB - International Joint Conferences on Artificial Intelligence
T2 - 32nd International Joint Conference on Artificial Intelligence, IJCAI 2023
Y2 - 19 August 2023 through 25 August 2023
ER -