Longest biased interval and longest non-negative sum interval

Longest Biased Interval and Longest Non-negative Sum Interval

UNLABELLED Described is an algorithm to find the longest interval having at least a specified minimum bias in a sequence of characters (bases, amino acids), e.g. 'at least 0.95 (A+T)-rich'. It is based on an algorithm to find the longest interval having a non-negative sum in a sequence of positive and negative numbers. In practice, it runs in linear time; this can be guaranteed if the bias is r...

The Longest Path Problem Is Polynomial on Interval Graphs

The longest path problem is the problem of finding a path of maximum length in a graph. Polynomial solutions for this problem are known only for small classes of graphs, while it is NP-hard on general graphs, as it is a generalization of the Hamiltonian path problem. Motivated by the work of Uehara and Uno in [22], where they left the longest path problem open for the class of interval graphs, ...

Polynomial Fixed-parameter Algorithms: A Case Study for Longest Path on Interval Graphs

We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus on a fundamental graph problem: Longest Path, that is, given an undirected graph, find a maximum-length path in G. Longest Path is NP-hard in general but kno...

Estimation of Longest Stability Interval for a Kind of Explicit Linear Multistep Methods

Highly non-concurrent longest paths in lattices

Yasir BASHIR1,∗, Faisal NADEEM, Ayesha SHABBIR Faculty of Mathematics, COMSATS Institute of Information Technology Wah Campus, Wah Cantt, Pakistan Faculty of Mathematics, COMSATS Institute of Information Technology Lahore Campus, Lahore, Pakistan Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore, Pakistan University College of Engineering, Sciences and Te...