1,151 research outputs found
Reliable experimental quantification of bipartite entanglement without reference frames
Simply and reliably detecting and quantifying entanglement outside laboratory
conditions will be essential for future quantum information technologies. Here
we address this issue by proposing a method for generating expressions which
can perform this task between two parties who do not share a common reference
frame. These reference frame independent expressions only require simple local
measurements, which allows us to experimentally test them using an
off-the-shelf entangled photon source. We show that the values of these
expressions provide bounds on the concurrence of the state, and demonstrate
experimentally that these bounds are more reliable than values obtained from
state tomography since characterizing experimental errors is easier in our
setting. Furthermore, we apply this idea to other quantities, such as the Renyi
and von Neumann entropies, which are also more reliably calculated directly
from the raw data than from a tomographically reconstructed state. This
highlights the relevance of our approach for practical quantum information
applications that require entanglement
Algorithms for Secretary Problems on Graphs and Hypergraphs
We examine several online matching problems, with applications to Internet
advertising reservation systems. Consider an edge-weighted bipartite graph G,
with partite sets L, R. We develop an 8-competitive algorithm for the following
secretary problem: Initially given R, and the size of L, the algorithm receives
the vertices of L sequentially, in a random order. When a vertex l \in L is
seen, all edges incident to l are revealed, together with their weights. The
algorithm must immediately either match l to an available vertex of R, or
decide that l will remain unmatched.
Dimitrov and Plaxton show a 16-competitive algorithm for the transversal
matroid secretary problem, which is the special case with weights on vertices,
not edges. (Equivalently, one may assume that for each l \in L, the weights on
all edges incident to l are identical.) We use a similar algorithm, but
simplify and improve the analysis to obtain a better competitive ratio for the
more general problem. Perhaps of more interest is the fact that our analysis is
easily extended to obtain competitive algorithms for similar problems, such as
to find disjoint sets of edges in hypergraphs where edges arrive online. We
also introduce secretary problems with adversarially chosen groups. Finally, we
give a 2e-competitive algorithm for the secretary problem on graphic matroids,
where, with edges appearing online, the goal is to find a maximum-weight
acyclic subgraph of a given graph.Comment: 15 pages, 2 figure
Keyword Search on RDF Graphs - A Query Graph Assembly Approach
Keyword search provides ordinary users an easy-to-use interface for querying
RDF data. Given the input keywords, in this paper, we study how to assemble a
query graph that is to represent user's query intention accurately and
efficiently. Based on the input keywords, we first obtain the elementary query
graph building blocks, such as entity/class vertices and predicate edges. Then,
we formally define the query graph assembly (QGA) problem. Unfortunately, we
prove theoretically that QGA is a NP-complete problem. In order to solve that,
we design some heuristic lower bounds and propose a bipartite graph
matching-based best-first search algorithm. The algorithm's time complexity is
, where is the number of the keywords and is a
tunable parameter, i.e., the maximum number of candidate entity/class vertices
and predicate edges allowed to match each keyword. Although QGA is intractable,
both and are small in practice. Furthermore, the algorithm's time
complexity does not depend on the RDF graph size, which guarantees the good
scalability of our system in large RDF graphs. Experiments on DBpedia and
Freebase confirm the superiority of our system on both effectiveness and
efficiency
Diverse Weighted Bipartite b-Matching
Bipartite matching, where agents on one side of a market are matched to
agents or items on the other, is a classical problem in computer science and
economics, with widespread application in healthcare, education, advertising,
and general resource allocation. A practitioner's goal is typically to maximize
a matching market's economic efficiency, possibly subject to some fairness
requirements that promote equal access to resources. A natural balancing act
exists between fairness and efficiency in matching markets, and has been the
subject of much research.
In this paper, we study a complementary goal---balancing diversity and
efficiency---in a generalization of bipartite matching where agents on one side
of the market can be matched to sets of agents on the other. Adapting a
classical definition of the diversity of a set, we propose a quadratic
programming-based approach to solving a supermodular minimization problem that
balances diversity and total weight of the solution. We also provide a scalable
greedy algorithm with theoretical performance bounds. We then define the price
of diversity, a measure of the efficiency loss due to enforcing diversity, and
give a worst-case theoretical bound. Finally, we demonstrate the efficacy of
our methods on three real-world datasets, and show that the price of diversity
is not bad in practice
The Query-commit Problem
In the query-commit problem we are given a graph where edges have distinct
probabilities of existing. It is possible to query the edges of the graph, and
if the queried edge exists then its endpoints are irrevocably matched. The goal
is to find a querying strategy which maximizes the expected size of the
matching obtained. This stochastic matching setup is motivated by applications
in kidney exchanges and online dating.
In this paper we address the query-commit problem from both theoretical and
experimental perspectives. First, we show that a simple class of edges can be
queried without compromising the optimality of the strategy. This property is
then used to obtain in polynomial time an optimal querying strategy when the
input graph is sparse. Next we turn our attentions to the kidney exchange
application, focusing on instances modeled over real data from existing
exchange programs. We prove that, as the number of nodes grows, almost every
instance admits a strategy which matches almost all nodes. This result supports
the intuition that more exchanges are possible on a larger pool of
patient/donors and gives theoretical justification for unifying the existing
exchange programs. Finally, we evaluate experimentally different querying
strategies over kidney exchange instances. We show that even very simple
heuristics perform fairly well, being within 1.5% of an optimal clairvoyant
strategy, that knows in advance the edges in the graph. In such a
time-sensitive application, this result motivates the use of committing
strategies
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