@inproceedings{20159,
  abstract     = {{Let G = (V,E) be an undirected graph on n vertices with non-negative capacities on its edges. The mincut sensitivity problem for the insertion of an edge is defined as follows. Build a compact data structure for G and a given set S ⊆ V of vertices that, on receiving any edge (x,y) ∈ S×S of positive capacity as query input, can efficiently report the set of all pairs from S× S whose mincut value increases upon insertion of the edge (x,y) to G. The only result that exists for this problem is for a single pair of vertices (Picard and Queyranne, Mathematical Programming Study, 13 (1980), 8-16). We present the following results for the single source and the all-pairs versions of this problem. 
1) Single source: Given any designated source vertex s, there exists a data structure of size 𝒪(|S|) that can output all those vertices from S whose mincut value to s increases upon insertion of any given edge. The time taken by the data structure to answer any query is 𝒪(|S|). 
2) All-pairs: There exists an 𝒪(|S|²) size data structure that can output all those pairs of vertices from S× S whose mincut value gets increased upon insertion of any given edge. The time taken by the data structure to answer any query is 𝒪(k), where k is the number of pairs of vertices whose mincut increases. 
For both these versions, we also address the problem of reporting the values of the mincuts upon insertion of any given edge. To derive our results, we use interesting insights into the nearest and the farthest mincuts for a pair of vertices. In addition, a crucial result, that we establish and use in our data structures, is that there exists a directed acyclic graph of 𝒪(n) size that compactly stores the farthest mincuts from all vertices of V to a designated vertex s in the graph. We believe that this result is of independent interest, especially, because it also complements a previously existing result by Hariharan et al. (STOC 2007) that the nearest mincuts from all vertices of V to s is a laminar family, and hence, can be stored compactly in a tree of 𝒪(n) size.}},
  author       = {{Baswana, Surender and Gupta, Shiv and Knollmann, Till}},
  booktitle    = {{28th Annual European Symposium on Algorithms (ESA 2020)}},
  editor       = {{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter}},
  isbn         = {{978-3-95977-162-7}},
  issn         = {{1868-8969}},
  keywords     = {{Mincut, Sensitivity, Data Structure}},
  pages        = {{12:1--12:14}},
  publisher    = {{Schloss Dagstuhl -- Leibniz-Zentrum für Informatik}},
  title        = {{{Mincut Sensitivity Data Structures for the Insertion of an Edge}}},
  doi          = {{10.4230/LIPIcs.ESA.2020.12}},
  volume       = {{173}},
  year         = {{2020}},
}

@inproceedings{4411,
  abstract     = {{While a lot of research in distributed computing has covered solutions for self-stabilizing computing and topologies, there is far less work on self-stabilization for distributed data structures.
Considering crashing peers in peer-to-peer networks, it should not be taken for granted that a distributed data structure remains intact.
In this work, we present a self-stabilizing protocol for a distributed data structure called the hashed Patricia Trie (Kniesburges and Scheideler WALCOM'11) that enables efficient prefix search on a set of keys.
The data structure has a wide area of applications including string matching problems while offering low overhead and efficient operations when embedded on top of a distributed hash table.
Especially, longest prefix matching for $x$ can be done in $\mathcal{O}(\log |x|)$ hash table read accesses.
We show how to maintain the structure in a self-stabilizing way.
Our protocol assures low overhead in a legal state and a total (asymptotically optimal) memory demand of $\Theta(d)$ bits, where $d$ is the number of bits needed for storing all keys.}},
  author       = {{Knollmann, Till and Scheideler, Christian}},
  booktitle    = {{Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS)}},
  editor       = {{Izumi, Taisuke and Kuznetsov, Petr}},
  keywords     = {{Self-Stabilizing, Prefix Search, Distributed Data Structure}},
  location     = {{Tokyo}},
  publisher    = {{Springer, Cham}},
  title        = {{{A Self-Stabilizing Hashed Patricia Trie}}},
  doi          = {{10.1007/978-3-030-03232-6_1}},
  volume       = {{11201}},
  year         = {{2018}},
}