Related papers: The Floyd-Warshall Algorithm, the AP and the TSP I…
We improve proofs in "The Floyd-Warshall Algorithm, the AP and the TSP (III). We also simplify the method for obtaining a good upper bound for an optimal solution.
In math.CO/0111309, we used admissible permutations and a variant of the Floyd-Warshall Algorithm to obtain an optimal solution to the Assignment Problem and an approximate solution to the Traveling Salesman Problem. Here we give a large,…
We use admissible permutations and a variant of the Floyd-Warshall algorithm to obtain an optimal solution to the Assignment Problem. Using another variant of the F-W algorithm, we obtain an approximate solution to the Traveling Salesman…
The celebrated Floyd-Warshall algorithm efficiently computes the all-pairs shortest path, and its simplicity made it a staple in computer science classes. Frequently, students discover a variant of this Floyd-Warshall algorithm by mixing up…
The Floyd--Warshall algorithm is a well-known algorithm for the all-pairs shortest path problem that is simply implemented by triply nested loops. In this study, we show that the incorrect implementations of the Floyd--Warshall algorithm…
This is a revised version (replacing an older one) with typos fixed and the introduction expanded.
Classical Floyd-Warshall algorithm is used to solve all-pairs shortest path problem on a directed graph. The classical algorithm runs in \mathcal{O} (V^{3}) time where V represents the number of nodes. Here we have modified the algorithm…
We accelerate the computation of spherical harmonic transforms, using what is known as the butterfly scheme. This provides a convenient alternative to the approach taken in the second paper from this series on "Fast algorithms for spherical…
Based on the weighted and shifted Gr\"{u}nwald difference (WSGD) operators [24], we further construct the compact finite difference discretizations for the fractional operators. Then the discretization schemes are used to approximate the…
We present a new implementation of the Floyd-Warshall All-Pairs Shortest Paths algorithm on CUDA. Our algorithm runs approximately 5 times faster than the previously best reported algorithm. In order to achieve this speedup, we applied a…
Recent results on the calculation of 3-loop massive operator matrix elements in case of one and two heavy quark masses are reported. They concern the $O(n_f T_F^2 C_{F,A})$ and $O(T_F^2 C_{F,A})$ gluonic corrections, two-mass quarkonic…
We show that Boolean matrix multiplication, computed as a sum of products of column vectors with row vectors, is essentially the same as Warshall's algorithm for computing the transitive closure matrix of a graph from its adjacency matrix.…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
We propose and analyse new stabilized time marching schemes for Phase Fields model such as Allen-Cahn and Cahn-Hillard equations, when discretized in space with high order finite differences compact schemes. The stabilization applies to…
The algorithm reduces the running time of an algorithm of Frieze from O(n^{1.5)) to O(n^(4/3 + o)). It also introduces the concept of admissible permutations that is used in algorithms for obtaining solutions to the AP and the TSP.
By use of the threshold expansion we develop an algorithm for analytical evaluation, within dimensional regularization, of arbitrary terms in the expansion of the (two-loop) sunset diagram with general masses m_1, m_2 and m_3 near its…
We present the calculation of the mixed two-loop QCD/electroweak corrections to hadronic W boson decays within the Standard Model. The optical theorem is applied to the W boson two-point function. The multi-scale integrals are computed with…
This paper proposes a novel preconditioned implicit-explicit algorithm enhanced with the extrapolation technique for non-convex optimization problems. The algorithm employs a third-order Adams-Bashforth scheme for the nonlinear and explicit…
We consider the use of arbitrary phases in quantum amplitude amplification which is a generalization of quantum searching. We prove that the phase condition in amplitude amplification is given by $\tan(\varphi/2) = \tan(\phi/2)(1-2a)$,…
We show that there is a polynomial-time algorithm with approximation guarantee $\frac{3}{2}+\epsilon$ for the $s$-$t$-path TSP, for any fixed $\epsilon>0$. It is well known that Wolsey's analysis of Christofides' algorithm also works for…