14,149 research outputs found
Simplifying Random Satisfiability Problem by Removing Frustrating Interactions
How can we remove some interactions in a constraint satisfaction problem
(CSP) such that it still remains satisfiable? In this paper we study a modified
survey propagation algorithm that enables us to address this question for a
prototypical CSP, i.e. random K-satisfiability problem. The average number of
removed interactions is controlled by a tuning parameter in the algorithm. If
the original problem is satisfiable then we are able to construct satisfiable
subproblems ranging from the original one to a minimal one with minimum
possible number of interactions. The minimal satisfiable subproblems will
provide directly the solutions of the original problem.Comment: 21 pages, 16 figure
On Capturing the Spreading Dynamics over Trading Prices in the Market
While market is a social field where information flows over the interacting
agents, there have been not so many methods to observe the spreading
information in the prices comprising the market. By incorporating the entropy
transfer in information theory in its relation to the Granger causality, the
paper proposes a tree of weighted directed graph of market to detect the
changes of price might affect other price changes. We compare the proposed
analysis with the similar tree representation built from the correlation
coefficients of stock prices in order to have insight of possibility in seeing
the collective behavior of the market in general.Comment: 9 pages, 3 figure
Lipschitz Continuous Algorithms for Graph Problems
It has been widely observed in the machine learning community that a small
perturbation to the input can cause a large change in the prediction of a
trained model, and such phenomena have been intensively studied in the machine
learning community under the name of adversarial attacks. Because graph
algorithms also are widely used for decision making and knowledge discovery, it
is important to design graph algorithms that are robust against adversarial
attacks. In this study, we consider the Lipschitz continuity of algorithms as a
robustness measure and initiate a systematic study of the Lipschitz continuity
of algorithms for (weighted) graph problems.
Depending on how we embed the output solution to a metric space, we can think
of several Lipschitzness notions. We mainly consider the one that is invariant
under scaling of weights, and we provide Lipschitz continuous algorithms and
lower bounds for the minimum spanning tree problem, the shortest path problem,
and the maximum weight matching problem. In particular, our shortest path
algorithm is obtained by first designing an algorithm for unweighted graphs
that are robust against edge contractions and then applying it to the
unweighted graph constructed from the original weighted graph.
Then, we consider another Lipschitzness notion induced by a natural mapping
that maps the output solution to its characteristic vector. It turns out that
no Lipschitz continuous algorithm exists for this Lipschitz notion, and we
instead design algorithms with bounded pointwise Lipschitz constants for the
minimum spanning tree problem and the maximum weight bipartite matching
problem. Our algorithm for the latter problem is based on an LP relaxation with
entropy regularization
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