A Linear Time Algorithm for the k Maximal Sums Problem

by Gerth Stølting Brodal , Allan Grønlund Jørgensen

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Datum	Value	Source
TITLE	A Linear Time Algorithm for the k Maximal Sums Problem	SVM HeaderParse 0.2
AUTHOR NAME	Gerth Stølting Brodal	SVM HeaderParse 0.2
AUTHOR AFFIL	BRICS ⋆ ⋆ , MADALGO ⋆ ⋆ ⋆ , Department of Computer Science,	SVM HeaderParse 0.2
AUTHOR ADDR	University of Aarhus, Denmark.	SVM HeaderParse 0.2
AUTHOR NAME	Allan Grønlund Jørgensen	SVM HeaderParse 0.2
AUTHOR AFFIL	BRICS ⋆ ⋆ , MADALGO ⋆ ⋆ ⋆ , Department of Computer Science,	SVM HeaderParse 0.2
AUTHOR ADDR	University of Aarhus, Denmark.	SVM HeaderParse 0.2
ABSTRACT	Abstract. Finding the sub-vector with the largest sum in a sequence of n numbers is known as the maximum sum problem. Finding the k sub-vectors with the largest sums is a natural extension of this, and is known as the k maximal sums problem. In this paper we design an optimal O(n+k) time algorithm for the k maximal sums problem. We use this algorithm to obtain algorithms solving the two-dimensional k maximal sums problem in O(m 2 ·n+k) time, where the input is an m ×n matrix with m ≤ n. We generalize this algorithm to solve the d-dimensional problem in O(n 2d−1 +k) time. The space usage of all the algorithms can be reduced to O(n d−1 + k). This leads to the first algorithm for the k maximal sums problem in one dimension using O(n + k) time and O(k) space. 1	SVM HeaderParse 0.2
CITATIONS	22 found	ParsCit 1.0