Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bounds for distributed markov chain problems   We study the worst-case communication complexity of distributed algorithms
computing a path problem based on stationary distributions of random walks in a
network $G$ with the caveat that $G$ is also the communication network. The
problem is a natural generalization of shortest path lengths to expected path
lengths, and represents a model used in many practical applications such as
pagerank and eigentrust as well as other problems involving Markov chains
defined by networks.
  For the problem of computing a single stationary probability, we prove an
$\Omega(n^2 \log n)$ bits lower bound; the trivial centralized algorithm costs
$O(n^3)$ bits and no known algorithm beats this. We also prove lower bounds for
the related problems of approximately computing the stationary probabilities,
computing only the ranking of the nodes, and computing the node with maximal
rank. As a corollary, we obtain lower bounds for labelling schemes for the
hitting time between two nodes.

14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph