TY - GEN
T1 - Learning-Augmented Maximum Independent Set
AU - Braverman, Vladimir
AU - Dharangutte, Prathamesh
AU - Shah, Vihan
AU - Wang, Chen
N1 - Publisher Copyright:
© Vladimir Braverman, Prathamesh Dharangutte, Vihan Shah, and Chen Wang.
PY - 2024/9/1
Y1 - 2024/9/1
N2 - We study the Maximum Independent Set (MIS) problem on general graphs within the framework of learning-augmented algorithms. The MIS problem is known to be NP-hard and is also NP-hard to approximate to within a factor of n1−δ for any δ > 0. We show that we can break this barrier in the presence of an oracle obtained through predictions from a machine learning model that answers vertex membership queries for a fixed MIS with probability 1/2 + ε. In the first setting we consider, the oracle can be queried once per vertex to know if a vertex belongs to a fixed MIS, and the oracle returns the correct answer with probability 1/2 + ε. Under this setting, we show an algorithm that obtains an Oe(√∆/ε)1-approximation in O(m) time where ∆ is the maximum degree of the graph. In the second setting, we allow multiple queries to the oracle for a vertex, each of which is correct with probability 1/2 + ε. For this setting, we show an O(1)-approximation algorithm using O(n/ε2) total queries and Oe(m) runtime.
AB - We study the Maximum Independent Set (MIS) problem on general graphs within the framework of learning-augmented algorithms. The MIS problem is known to be NP-hard and is also NP-hard to approximate to within a factor of n1−δ for any δ > 0. We show that we can break this barrier in the presence of an oracle obtained through predictions from a machine learning model that answers vertex membership queries for a fixed MIS with probability 1/2 + ε. In the first setting we consider, the oracle can be queried once per vertex to know if a vertex belongs to a fixed MIS, and the oracle returns the correct answer with probability 1/2 + ε. Under this setting, we show an algorithm that obtains an Oe(√∆/ε)1-approximation in O(m) time where ∆ is the maximum degree of the graph. In the second setting, we allow multiple queries to the oracle for a vertex, each of which is correct with probability 1/2 + ε. For this setting, we show an O(1)-approximation algorithm using O(n/ε2) total queries and Oe(m) runtime.
KW - Learning-augmented algorithms
KW - graph algorithms
KW - maximum independent set
UR - https://www.scopus.com/pages/publications/85204428376
U2 - 10.4230/LIPIcs.APPROX/RANDOM.2024.24
DO - 10.4230/LIPIcs.APPROX/RANDOM.2024.24
M3 - Conference contribution
AN - SCOPUS:85204428376
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2024
A2 - Kumar, Amit
A2 - Ron-Zewi, Noga
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 27th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2024 and the 28th International Conference on Randomization and Computation, RANDOM 2024
Y2 - 28 August 2024 through 30 August 2024
ER -