Algorithm for K Disjoint Maximum Subarrays

Algorithm for K Disjoint Maximum Subarrays

The maximum subarray problem is to find the array portion that maximizes the sum of array elements in it. For K disjoint maximum subarrays, Ruzzo and Tompa gave an O(n) time solution for one-dimension. This solution is, however, difficult to extend to two-dimensions. While a trivial solution of O(Kn...

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Bibliographische Detailangaben
Hauptverfasser: Bae, Sung Eun, Takaoka, Tadao
Format: Buchkapitel
Sprache:eng
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Array Element
Computer science
control theory
systems
Exact sciences and technology
Input Array
Small Physical Size
Theoretical computing
Time Solution
Trivial Solution
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Beschreibung
Zusammenfassung:The maximum subarray problem is to find the array portion that maximizes the sum of array elements in it. For K disjoint maximum subarrays, Ruzzo and Tompa gave an O(n) time solution for one-dimension. This solution is, however, difficult to extend to two-dimensions. While a trivial solution of O(Kn3) time is easily obtainable for two-dimensions, little study has been undertaken to better this. We first propose an O(n+Klog K) time solution for one-dimension. This is equivalent to Ruzzo and Tompa’s when order is considered. Based on this, we achieve O(n3+Kn2log n) time for two-dimensions. This is cubic time when K≤ n/log n.
ISSN:0302-9743
1611-3349
DOI:10.1007/11758501_80