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Maximum subarray problems arise in many fields, such as genomic sequence analysis and computer vision.. Genomic sequence analysis employs maximum subarray algorithms to identify important biological segments of protein sequences that have unusual properties, by assigning scores to points within the sequence that are positive when a motif to be recognized is present, and negative when it is not ...
Identifying the in-place algorithms with L has some interesting implications; for example, it means that there is a (rather complex) in-place algorithm to determine whether a path exists between two nodes in an undirected graph, [3] a problem that requires O(n) extra space using typical algorithms such as depth-first search (a visited bit for ...
The maximum clique problem is the special case in which all weights are equal. [15] As well as the problem of optimizing the sum of weights, other more complicated bicriterion optimization problems have also been studied. [16] In the maximal clique listing problem, the input is an undirected graph, and the output is a list of all its maximal ...
Illustration of Dijkstra's algorithm finding a path from a start node (lower left, red) to a target node (upper right, green) in a robot motion planning problem. Open nodes represent the "tentative" set (aka set of "unvisited" nodes). Filled nodes are the visited ones, with color representing the distance: the redder, the closer (to the start ...
In the subset sum problem, the goal is to find a subset of S whose sum is a certain target number T given as input (the partition problem is the special case in which T is half the sum of S). In multiway number partitioning , there is an integer parameter k , and the goal is to decide whether S can be partitioned into k subsets of equal sum ...
The query algorithm visits one node per level of the tree, so O(log n) nodes in total. On the other hand, at a node v, the segments in I are reported in O(1 + k v) time, where k v is the number of intervals at node v, reported. The sum of all the k v for all nodes v visited, is k, the number of reported segments. [5]
The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers and a target-sum T {\displaystyle T} , and the question is to decide whether any subset of the integers sum to precisely T {\displaystyle T} . [ 1 ]
For an arbitrary number of input sequences, the dynamic programming approach gives a solution in O ( N ∏ i = 1 N n i ) . {\displaystyle O\left(N\prod _{i=1}^{N}n_{i}\right).} There exist methods with lower complexity, [ 3 ] which often depend on the length of the LCS, the size of the alphabet, or both.