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research-article
January 2020
Connectivity Oracles for Graphs Subject to Vertex Failures
- Ran Duan,
- Seth Pettie
SIAM Journal on Computing (SICOMP), Volume 49, Issue 62020, Pages 1363–1396https://doi.org/10.1137/17M1146610

We introduce new data structures for answering connectivity queries in graphs subject to batched vertex failures. A deterministic structure processes a batch of $d\leq d_\star$ failed vertices in $\tilde{O}(d^3)$ time and thereafter answers connectivity ...
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research-article
January 2020
Bidimensionality and Kernels
SIAM Journal on Computing (SICOMP), Volume 49, Issue 62020, Pages 1397–1422https://doi.org/10.1137/16M1080264

Bidimensionality theory was introduced by [E. D. Demaine et al., J. ACM, 52 (2005), pp. 866--893] as a tool to obtain subexponential time parameterized algorithms on H-minor-free graphs. In [E. D. Demaine and M. Hajiaghayi, Bidimensionality: New ...
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