by Yossi Azar, Andrei Z. Broder, Anna R. Karlin, Nathan Linial, Steven Phillips
http://www.math.tau.ac.il/~azar/walk.ps.gz
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Abstract:
How much can an imperfect source of randomness affect an algorithm? We examine several simple questions of this type concerning the long-term behavior of a random walk on a finite graph. In our setup, at each step of the random walk a "controller " can, with a certain small probability, fix the next step, thus introducing a bias. We analyze the extent to which the bias can affect the limit behavior of the walk. The controller is assumed to associate a real, nonnegative, "benefit " with each state, and to strive to maximize the long-term expected benefit. We derive tight bounds on the maximum of this objective function over all controller's strategies, and present polynomial time algorithms for computing the optimal controller strategy. 1
Citations
|
1120
|
Equation of state calculations by fast computing machines
– Metropolis, Rosenbluth, et al.
- 1953
|
|
645
|
Perturbation theory for linear operators
– Kato
- 1980
|
|
167
|
How to recycle random bits
– Impagliazzo, Zuckerman
- 1989
|
|
82
|
Dispersers, deterministic amplification, and weak random sources
– Cohen, Wigderson
- 1989
|
|
63
|
Generating quasi-random sequences from semi-random sources
– Santha, Vazirani
- 1986
|
|
59
|
Collective coin flipping
– Ben-Or, Linial
- 1990
|
|
45
|
Randomness, Adversaries and Computation
– Vazirani
- 1986
|
|
34
|
Deterministic simulation
– Ajtai, Komlos, et al.
- 1987
|
|
27
|
Fault-tolerant computation in the full information model
– Goldreich, Goldwasser, et al.
- 1998
|
|
23
|
Perturbation Theory of Eigenvalue Problems
– Rellich
- 1969
|
|
20
|
Finite State Markov Decision Processes
– Derman
- 1970
|
|
16
|
The influence of large coalitions
– Ajtai, Linial
- 1993
|
|
15
|
Some extremal problems arising from discrete control processes
– Lichtenstein, Linial, et al.
- 1989
|
|
12
|
Coin-flipping games immune against linear-sized coalitions
– Alon, Naor
- 1993
|
|
12
|
Biased Random Walks
– Azar, Broder, et al.
- 1992
|
|
12
|
Collective coin flipping and other models of imperfect randomness
– Ben-Or, Linial, et al.
- 1987
|
|
10
|
Biased coins and randomized algorithms
– Alon, Rabin
- 1989
|
|
10
|
Perturbation Methods
– Hinch
- 1991
|
|
1
|
Efficiency Considerations in Using Slightly-Random Sources
– Vazirani
- 1987
|
