This paper presents the computational complexity of finding maximal elements in a set of d-dimensional vectors. The problem involves determining the maximum number of comparisons required to identify all maximal elements in a set of n vectors, where each vector is a d-tuple from totally ordered sets. The computational complexity is denoted by $ C_d(n) $, which represents the worst-case number of comparisons needed. For $ d = 2 $ and $ d = 3 $, it is shown that $ C_d(n) = O(n \log n) $. For $ d \geq 4 $, the complexity is bounded by $ C_d(n) \leq O(n (\log n)^{d-2}) $. Additionally, a lower bound of $ \log n $ is established for $ d \geq 2 $, indicating that at least $ \log n $ comparisons are required in the worst case. The paper also provides algorithms for $ d = 2 $ and $ d = 3 $ that achieve the upper bounds of $ O(n \log n) $. For $ d > 3 $, a general algorithm is described that uses a recursive approach, dividing the problem into smaller subproblems and combining their results. The complexity of this algorithm is shown to be $ O(n (\log n)^{d-2}) $ for $ d \geq 4 $. The results are derived using a combination of information-theoretic arguments and recursive techniques. The paper also discusses the relationship between the complexity of finding maxima in different dimensions and provides a detailed analysis of the algorithms used to achieve these bounds. The work builds on previous research and contributes to the understanding of the computational complexity of finding maxima in multi-dimensional vector sets.This paper presents the computational complexity of finding maximal elements in a set of d-dimensional vectors. The problem involves determining the maximum number of comparisons required to identify all maximal elements in a set of n vectors, where each vector is a d-tuple from totally ordered sets. The computational complexity is denoted by $ C_d(n) $, which represents the worst-case number of comparisons needed. For $ d = 2 $ and $ d = 3 $, it is shown that $ C_d(n) = O(n \log n) $. For $ d \geq 4 $, the complexity is bounded by $ C_d(n) \leq O(n (\log n)^{d-2}) $. Additionally, a lower bound of $ \log n $ is established for $ d \geq 2 $, indicating that at least $ \log n $ comparisons are required in the worst case. The paper also provides algorithms for $ d = 2 $ and $ d = 3 $ that achieve the upper bounds of $ O(n \log n) $. For $ d > 3 $, a general algorithm is described that uses a recursive approach, dividing the problem into smaller subproblems and combining their results. The complexity of this algorithm is shown to be $ O(n (\log n)^{d-2}) $ for $ d \geq 4 $. The results are derived using a combination of information-theoretic arguments and recursive techniques. The paper also discusses the relationship between the complexity of finding maxima in different dimensions and provides a detailed analysis of the algorithms used to achieve these bounds. The work builds on previous research and contributes to the understanding of the computational complexity of finding maxima in multi-dimensional vector sets.