Path algebra algorithm for finding longest increasing subsequence
نویسنده
چکیده
New algorithm for finding longest increasing subsequence is discussed. This algorithm is based on the ideas of idempotent mathematic and uses Max-Plus idempotent semiring. Problem of finding longest increasing subsequence is reformulated in a matrix form and solved with linear algebra.
منابع مشابه
Finding a Longest Increasing Subsequence from the Paths in a Complete Bipartite Graph∗
Let S = s1, s2, . . . , sn be an integer sequence. The longest increasing subsequence problem is to find an increasing subsequence of S with the longest length. By regarding S as a weight sequence of the vertices in a path, we can redefine the longest increasing subsequence problem on graphs as follows. Let G = (V,E) be a graph in which every vertex v ∈ V has a weight w(v). A longest increasing...
متن کاملFinding Longest Common Increasing Subsequence for Two Different Scenarios of Non-random Input Sequences
By reviewing Longest Increasing Subsequence (LIS) and Longest Common Subsequence (LCS), the Longest Common Increasing Subsequence (LCIS) problem is explored for two non-random input cases in details. Specifically, we designed two algorithms, one solving the input sequence scenario with the case that one sequence is ordered and duplicate elements are allowed in each of sequences, and the second ...
متن کاملOn Some Variants of the Longest Increasing Subsequence Problem
The problem of finding a longest increasing subsequence (LIS) is a well known task in sequence processing. There are many variants of the basic task. We discuss a recently introduced variant of LIS, a minimal height longest increasing subsequence problem and propose a new algorithm for it, which improves its time complexity. Moreover, we define a family of similar problems and introduce algorit...
متن کاملAn Optimal Algorithm for Finding the Longest Increasing Subsequence of Every Substring
Given a string S = {a1, a2, a3, · · · , an}, the longest increasing subsequence (LIS) problem is to find a subsequence of the given string such that the subsequence is increasing and its length is maximal. In a previous result, to find the longest increasing subsequences of each sliding windows with a fixed size w of a given string can be solved in O(w log log n + OUTPUT ) time, where O(w log l...
متن کاملA simple linear space algorithm for computing a longest common increasing subsequence
This paper reformulates the problem of finding a longest common increasing subsequence of the two given input sequences in a very succinct way. An extremely simple linear space algorithm based on the new formula can find a longest common increasing subsequence of sizes n and m respectively, in time O(nm) using additional min{n,m}+ 1 space.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1409.2928 شماره
صفحات -
تاریخ انتشار 2014