Przemyslaw Uznanski: A Framework for Searching in Graphs in the Presence of Errors
01 June 2018
Manno, Galleria 1, 2nd floor, room G1-204 @12:00
We consider two types of searching models, where the goal is to design
an adaptive algorithm that locates an unknown vertex in a graph by
repeatedly performing queries. In the vertex-query model, each query
points to a vertex v and the response either admits that v is the
target or provides a neighbor of von a shortest path from v to the
target. This model has been introduced for trees by Onak and Parys
[FOCS 2006] and by Emamjomeh-Zadeh et al. [STOC 2016] for arbitrary
graphs. In the edge-query model, each query chooses an edge and the
response reveals which endpoint of the edge is closer to the target,
breaking ties arbitrarily.
Our goal is to analyze solutions to these problems assuming that some
responses may be erroneous. We develop a scheme for tackling such
noisy models with the following line of arguments: For each of the two
models, we analyze a generic strategy that assumes a fixed number of
lies and give a precise bound for its length via an amortized
analysis. From this, we derive bounds for both a linearly bounded
error rate, where the number of errors in T queries is bounded by r*T
for some r<1/2, and a probabilistic model in which each response is
incorrect with some probability p<1/2. The bounds for adversarial case
turn out to be strong enough for non-adversarial scenarios as well.
We obtain thus a much simpler strategy performing fewer vertex-queries
than one by Emamjomeh-Zadeh et al. For edge-queries, not studied
before for general graphs, we obtain bounds that are tight up to log=CE=94
factors in all error models. Applying our graph-theoretic results to
the setting of edge-queries for paths, we obtain a number of
improvements over existing bounds for searching in a sorted array in
the presence of errors, including an exponential improvement for the
prefix-bounded model in unbounded domains.

The speaker

Przemyslaw Uznanski received a PhD from INRIA Bordeaux in 2013. He is a postdoc at ETH Zurich since 2015. He works on distributed computing, biological algorithms, graph algorithms and text processing (with emphasis on algebraic methods in algorithms).

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