LIS using backtracking and branch-and-bound approaches

• Published in: CSI TRANSACTIONS ON ICT Vol. 4; no. 2-4; pp. 87 - 93
• Main Authors: Rani, Seema, Rajpoot, Dharmveer Singh
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 2016; Springer Nature B.V
• Subjects: Computer Communication Networks; Computer Science; Input/Output and Data Communications; Integers; Parallel processing; Software Engineering/Programming and Operating Systems; Special Issue REDSET 2016 of CSIT; Systems and Data Security; Backtracking; Branch-and-bound; Longest increasing subsequence (LIS); Breadth first search (BFS); Depth first search (DFS)
• ISSN: 2277-9078; 2277-9086
• DOI: 10.1007/s40012-016-0108-x

Finding the longest increasing subsequence and its length from a sequence of finite integers is an NP-hard problem. Many significant efforts have been put to provide solutions to this problem with time complexity O(n log n) (n is the size of sequence), O(n 2 ), O(n log log k), O(n) (using parallel processing) and more. In this paper we provide conceptual views of LIS and its solution using two approaches—backtracking and branch-and-bound. Its implementation using backtracking approach takes time O(2 n ) and the other solution based on the concept of branch-and-bound approach takes O(n 2 ) time. Both solutions are efficient than the bruit force approach.