633 research outputs found
Two-batch liar games on a general bounded channel
We consider an extension of the 2-person R\'enyi-Ulam liar game in which lies
are governed by a channel , a set of allowable lie strings of maximum length
. Carole selects , and Paul makes -ary queries to uniquely
determine . In each of rounds, Paul weakly partitions and asks for such that . Carole responds with some
, and if , then accumulates a lie . Carole's string of
lies for must be in the channel . Paul wins if he determines within
rounds. We further restrict Paul to ask his questions in two off-line
batches. We show that for a range of sizes of the second batch, the maximum
size of the search space for which Paul can guarantee finding the
distinguished element is as ,
where is the number of lie strings in of maximum length . This
generalizes previous work of Dumitriu and Spencer, and of Ahlswede, Cicalese,
and Deppe. We extend Paul's strategy to solve also the pathological liar
variant, in a unified manner which gives the existence of asymptotically
perfect two-batch adaptive codes for the channel .Comment: 26 page
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
A power efficient method against misbehaving node in reputation system to prevent sybil attack in mobile ad-hoc network
Mobile ad-hoc network has become a very important field of study for students and researchers owing to its wide application. In mobile ad-hoc network all nodes are responsible for routing and forwarding of packets, hence all nodes are required to act selflessly for proper functioning of mobile ad-hoc network. The presence of selfish behavior in a node can degrade the performance of the mobile ad hoc network to a large extent. Several works have been done for identification and punishment of the misbehaving nodes in mobile ad hoc network. We propose here a method where some selected neighbors are participated in detecting misbehaving nodes in power effective manners. These neighbors participating in selfish node detection are chosen randomly. It also alerts all other nodes about the misbehaving links in the network. The simulation studies show that this does the job efficiently with less power consumption in the network. The power effectiveness of the algorithm also reduces the number of misbehaving nodes because many nodes show misbehavior to save their power
Succinct data structures for dynamics strings
A new simple algorithm for optimal embedding of complete binary trees into hypercubes as well as a node-by-node algorithm for embedding of nearly complete binary trees into hypercubes are presented
Sixth annual conference on alaskan placer mining
An abridged format of papers, presentations and addresses given during the 1984 conference held on March 28-29, 1984, compiled and edited by Daniel E. Walsh and M. Susan Wray
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