A randomized data structure for undirected weighted graphs that are partially dynamic, i.e., that undergo either only edge insertions or only edge deletions is given, which follows from a simple stability principle for partially dynamic graphs.
It is proved that the problem of defining a bounded cost set of nodes S such that the influence spreading from S in G, within a given time bound, is as large as possible, and that the problem is NP-hard, even in simple networks like complete graphs and trees.
Investigating the energy complexity of several well-studied (local) problems in distributed graph algorithms—namely, matching and vertex cover approximations, spanners, low-outdegree orientations, and set cover, presents randomized distributed algorithms that achieve nearly exponentially smaller energy complexity.
This paper provides a tight reduction demonstrating that any exact distance sensitivity oracle can be used to efficiently solve decremental exact diameter and all-node eccentricities and introduces two new instructive techniques and demonstrates how to utilize them to construct several new algorithms.
A new $O(\log n)$ approximation algorithm for Node Weighted Steiner Tree and Node Weighted Steiner Forest that matches the bounds of Klein&Ravi, but has the advantage that they work in the online setting when the terminal pairs are revealed in random order.
This paper generalises the existing PTAS for complete graphs from a fixed to an arbitrary number of intervals and disprove an existing conjecture, which states that every instance of BIA admits a solution satisfying at least three quarters of all edges.
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