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We give a polynomial time algorithm for finding optimal Nash equilibria.
The FPTAS is obtained despite the fact that we could not design a pseudo-polynomial time algorithm for finding the optimal solution.
We analyze the structure of landmark sets for trees and design a linear time algorithm for finding a minimum cost landmark set for a given tree graph.
Also, we propose an O(n log n + nk + k2 log k α k)) time algorithm for finding the smallest AABB under the assumption that the regions are disjoint.
We present a set of basic data movement algorithms for ORM and, as an applicate example, outline an O log N) time algorithm for finding the convex hulls of all figures in an N×N digitized image.
Apart from this, we design a polynomial time algorithm for finding γ(1,j)(G) for a fixed j in a split graph, and show that (1,j -set problem is fixed parameter tractable in bounded genus graphs and bounded treewidth graphs.
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Further, we propose O(n2k log nk) α nk)) time algorithms for finding the closest and furthest pair problems, and present a lower bound of Ω(n2) for the closest pair problem when k is constant.
For each of the problems considered, they use depth-first search to give linear time algorithms for finding the orientations or determine that they do not exist.
These results lead to polynomial time algorithms for finding the clique-colouring and the clique-chromatic number of the above classes.
We investigate certain properties of both models, propose a combinatorial branch-and-bound algorithm to find a maximum biconnected 2-club, and design a polynomial-time algorithm for finding a maximum fragile 2-club in a given graph.
This work uses a linear-time algorithm for finding paths in a network under modified biologically motivated constraints.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com