• The all-pairs shortest paths problem on weighted digraphs (APSP). • Detecting if a weighted graph has a triangle of negative total edge weight. • Listing up to n2.99 negative triangles in an edge-weighted graph. • Finding a minimum weight cycle in a graph of non-negative edge weights. • The replacement paths problem on weighted digraphs. • Finding the second shortest simple path between two n...

We address the problem of single-source shortest path computation in digraphs with non-negative edge weights subjected to frequent edge weight decreases such that only some shortest paths are requested in-between updates. We optimise a recent semidynamic algorithm for weight decreases previously reported to be the fastest one in various conditions, resulting in important time savings that we de...

This paper presents a new deterministic algorithm for decremental maintenance of the transitive closure in a directed graph. The algorithm processes any sequence of edge deletions in O(mn) time and answers queries in constant time. Until now such time bound has only been achieved by a randomized Las Vegas algorithm. In addition to that, a few decremental algorithms for maintaining strongly conn...

We prove that the minimum weight of a dicycle is equal to the maximum number of disjoint dicycle covers, for every weighted digraph whose underlying graph is planar and does not have K5 − e as a minor (K5 − e is the complete graph on five vertices, minus one edge). Equality was previously known when forbidding K4 as a minor, while an infinite number of weighted digraphs show that planarity does...

Models of complex information processing based on artificial neural networks frequently apply fully connected or random graph structures. However, it is well known that biological neural systems operate on sparsely connected networks having properties quite distinct to random graphs. In this paper, a simple method is introduced for the deterministic generation of strongly connected digraphs. Th...

Mader (1985) proved that every strongly $k$-connected $n$-vertex digraph contains a strongly $k$-connected spanning subgraph with at most $2kn - 2k^2$ edges, and this is sharp. For dense strongly $k$-connected digraphs, the bound can be significantly improved for dense strongly $k$-connected digraphs. Let $\overline{\Delta}(D)$ be the maximum degree of the complement of the underlying undirecte...