Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Hardness of Partially Dynamic Graph Problems and Connections to
  Diameter   Conditional lower bounds for dynamic graph problems has received a great deal
of attention in recent years. While many results are now known for the
fully-dynamic case and such bounds often imply worst-case bounds for the
partially dynamic setting, it seems much more difficult to prove amortized
bounds for incremental and decremental algorithms. In this paper we consider
partially dynamic versions of three classic problems in graph theory. Based on
popular conjectures we show that:
  -- No algorithm with amortized update time $O(n^{1-\varepsilon})$ exists for
incremental or decremental maximum cardinality bipartite matching. This
significantly improves on the $O(m^{1/2-\varepsilon})$ bound for sparse graphs
of Henzinger et al. [STOC'15] and $O(n^{1/3-\varepsilon})$ bound of Kopelowitz,
Pettie and Porat. Our linear bound also appears more natural. In addition, the
result we present separates the node-addition model from the edge insertion
model, as an algorithm with total update time $O(m\sqrt{n})$ exists for the
former by Bosek et al. [FOCS'14].
  -- No algorithm with amortized update time $O(m^{1-\varepsilon})$ exists for
incremental or decremental maximum flow in directed and weighted sparse graphs.
No such lower bound was known for partially dynamic maximum flow previously.
Furthermore no algorithm with amortized update time $O(n^{1-\varepsilon})$
exists for directed and unweighted graphs or undirected and weighted graphs.
  -- No algorithm with amortized update time $O(n^{1/2 - \varepsilon})$ exists
for incremental or decremental $(4/3-\varepsilon')$-approximating the diameter
of an unweighted graph. We also show a slightly stronger bound if node
additions are allowed. [...]

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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: math
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th