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.
Given a directed graph with positive edge weights and two vertices s,t, a next-to-shortest s-t path is a shortest simple s-t path among those whose length is strictly larger than the shortest-path distance. The problem was introduced by Lalgudi, Papaefthymiou and Potkonjak in 1996; it is NP-hard when zero-weight edges...
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.
This work studies the unambiguous complexity of the Long Path problem on DAGs under parameterization and obtains an algorithm that achieves unambiguous and co-unambiguous O ( k log n ) space while running in time polynomial in both n and k.
It is shown that the problem is PSPACE -complete on oriented graphs, NP -complete on directed acyclic graphs (DAGs), and W -hard on DAGs when parameterized by k, and the NP -completeness of the bounded-length variant on DAGs is proved.
An index structure that, for a temporal graph with N edges, requires O(N) space and can evaluate extended BGPs in wco time and yields wco guarantees for related query types, including snapshot evaluation, version queries, and other temporal variants.
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