TL;DR
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.
This paper presents an $\frac{11}{6} \approx 1.83$-competitive algorithm for trees in the more general edge arrival model and gives a 1.5-competitive algorithm and provide a matching lower bound.
It is proved that Minimal-to-Maximal Conversion Search is in fact not output-polynomial and the lower bound construction motivates a more detailed analysis of how certain heuristic choices in the algorithm design affect the running time.
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.
For graph instances both for the min-max and the min-disagreement objectives, this work proves approximation guarantees that are substantially better than the bounds achievable for general graphs.
Small boundary (SB(k)), a family of linear-time greedy heuristics that guide vertex labeling through a prioritization scheme based on the structure of labeled and k levels of unlabeled vertex neighborhoods, is introduced.
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