Under the APSP conjecture, no algorithm solves the narrow core in O ( m √ n polylog( nC )) time for all polynomially bounded integer costs: the decomposition confines the known hardness of 2-SP to a small, explicitly described class of detours.
It is shown that bidirectional Dijkstra is still instance-optimal on simple undirected weighted graphs under the order-oblivious model, where incident edges are given in a random order, and under the order-dependent model, where bidirectional Dijkstra is not instance-optimal.
Christian Bertram, Mads Vestergaard Jensen, Mikkel Thorup et al.· 1 citation
It is proved that the classical cut property always produces a minimum spanning tree of a connected graph, and may be useful for large weighted networks such as communication networks, wiring connections, and transportation networks.
H. Bhapkar, Rezwan Ul Shaban, S. Mir et al.· Journal of the Nigerian Soci...· 1 citation
Centroids are used to compute an arbitrary number of simple paths with some important benefits: the expansion of a single centroid delivers an arbitrary number of paths; only a single Dijk-stra search is required to complete the task; the same algorithm can be easily coupled with heuristics that improve search efficien...
Carlos Linares López, I. Herman· Proceedings of the Thirty-Fi...· 0 citations
The E2 Algorithm for constructing the Hamiltonian cycle in an arbitrary graph without edges’ weights is proposed and whether some general graphs are Hamiltonian is shown, to prove the correctness of the method.
Fatih Okumuş, A. Karadoğan· Fırat Üniversitesi Mühendisl...· 0 citations
Enumerating simple paths and cycles subject to a given length bound is a fundamental problem in graph algorithms. Recent algorithms, namely BC-DFS (Peng et al. 2019, 2021) and CYCLE_SEARCH (Gupta and Suzumura 2021, arXiv:2105.10094v2), employ cached barrier values to prune fruitless searches. Both algorithms turn out t...
Frank Bauernöppel, J. Sack· arXiv.org· 0 citations
Suppose that T is a normal spanning tree (depth-first search tree) of a graph G. If e=xy and e′=uv are edges of G, satisfying x≺Tu≺Ty≺Tv, then they are called secant edges of G with respect to T. Suppose that G has no secant edges with respect to T. If T is a path, Ghazal and Al-Mniny proved that the chromatic number i...
Salman Ghazal· AppliedMath· 0 citations
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