23,318 research outputs found
Query Learning with Exponential Query Costs
In query learning, the goal is to identify an unknown object while minimizing
the number of "yes" or "no" questions (queries) posed about that object. A
well-studied algorithm for query learning is known as generalized binary search
(GBS). We show that GBS is a greedy algorithm to optimize the expected number
of queries needed to identify the unknown object. We also generalize GBS in two
ways. First, we consider the case where the cost of querying grows
exponentially in the number of queries and the goal is to minimize the expected
exponential cost. Then, we consider the case where the objects are partitioned
into groups, and the objective is to identify only the group to which the
object belongs. We derive algorithms to address these issues in a common,
information-theoretic framework. In particular, we present an exact formula for
the objective function in each case involving Shannon or Renyi entropy, and
develop a greedy algorithm for minimizing it. Our algorithms are demonstrated
on two applications of query learning, active learning and emergency response.Comment: 15 page
A self-adapting latency/power tradeoff model for replicated search engines
For many search settings, distributed/replicated search engines deploy a large number of machines to ensure efficient retrieval. This paper investigates how the power consumption of a replicated search engine can be automatically reduced when the system has low contention, without compromising its efficiency. We propose a novel self-adapting model to analyse the trade-off between latency and power consumption for distributed search engines. When query volumes are high and there is contention for the resources, the model automatically increases the necessary number of active machines in the system to maintain acceptable query response times. On the other hand, when the load of the system is low and the queries can be served easily, the model is able to reduce the number of active machines, leading to power savings. The model bases its decisions on examining the current and historical query loads of the search engine. Our proposal is formulated as a general dynamic decision problem, which can be quickly solved by dynamic programming in response to changing query loads. Thorough experiments are conducted to validate the usefulness of the proposed adaptive model using historical Web search traffic submitted to a commercial search engine. Our results show that our proposed self-adapting model can achieve an energy saving of 33% while only degrading mean query completion time by 10 ms compared to a baseline that provisions replicas based on a previous day's traffic
Deterministic and Probabilistic Binary Search in Graphs
We consider the following natural generalization of Binary Search: in a given
undirected, positively weighted graph, one vertex is a target. The algorithm's
task is to identify the target by adaptively querying vertices. In response to
querying a node , the algorithm learns either that is the target, or is
given an edge out of that lies on a shortest path from to the target.
We study this problem in a general noisy model in which each query
independently receives a correct answer with probability (a
known constant), and an (adversarial) incorrect one with probability .
Our main positive result is that when (i.e., all answers are
correct), queries are always sufficient. For general , we give an
(almost information-theoretically optimal) algorithm that uses, in expectation,
no more than queries, and identifies the target correctly with probability at
leas . Here, denotes the
entropy. The first bound is achieved by the algorithm that iteratively queries
a 1-median of the nodes not ruled out yet; the second bound by careful repeated
invocations of a multiplicative weights algorithm.
Even for , we show several hardness results for the problem of
determining whether a target can be found using queries. Our upper bound of
implies a quasipolynomial-time algorithm for undirected connected
graphs; we show that this is best-possible under the Strong Exponential Time
Hypothesis (SETH). Furthermore, for directed graphs, or for undirected graphs
with non-uniform node querying costs, the problem is PSPACE-complete. For a
semi-adaptive version, in which one may query nodes each in rounds, we
show membership in in the polynomial hierarchy, and hardness
for
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