322,376 research outputs found
Complexity of the XY antiferromagnet at fixed magnetization
We prove that approximating the ground energy of the antiferromagnetic XY
model on a simple graph at fixed magnetization (given as part of the instance
specification) is QMA-complete. To show this, we strengthen a previous result
by establishing QMA-completeness for approximating the ground energy of the
Bose-Hubbard model on simple graphs. Using a connection between the XY and
Bose-Hubbard models that we exploited in previous work, this establishes
QMA-completeness of the XY model
Finite and infinite support in nominal algebra and logic: nominal completeness theorems for free
By operations on models we show how to relate completeness with respect to
permissive-nominal models to completeness with respect to nominal models with
finite support. Models with finite support are a special case of
permissive-nominal models, so the construction hinges on generating from an
instance of the latter, some instance of the former in which sufficiently many
inequalities are preserved between elements. We do this using an infinite
generalisation of nominal atoms-abstraction.
The results are of interest in their own right, but also, we factor the
mathematics so as to maximise the chances that it could be used off-the-shelf
for other nominal reasoning systems too. Models with infinite support can be
easier to work with, so it is useful to have a semi-automatic theorem to
transfer results from classes of infinitely-supported nominal models to the
more restricted class of models with finite support.
In conclusion, we consider different permissive-nominal syntaxes and nominal
models and discuss how they relate to the results proved here
Gap Amplification for Small-Set Expansion via Random Walks
In this work, we achieve gap amplification for the Small-Set Expansion
problem. Specifically, we show that an instance of the Small-Set Expansion
Problem with completeness and soundness is at least as
difficult as Small-Set Expansion with completeness and soundness
, for any function which grows faster than
. We achieve this amplification via random walks -- our gadget
is the graph with adjacency matrix corresponding to a random walk on the
original graph. An interesting feature of our reduction is that unlike gap
amplification via parallel repetition, the size of the instances (number of
vertices) produced by the reduction remains the same
The exchange-stable marriage problem
In this paper we consider instances of stable matching problems, namely the classical stable marriage (SM) and stable roommates (SR) problems and their variants. In such instances we consider a stability criterion that has recently been proposed, that of <i>exchange-stability</i>. In particular, we prove that ESM — the problem of deciding, given an SM instance, whether an exchange-stable matching exists — is NP-complete. This result is in marked contrast with Gale and Shapley's classical linear-time algorithm for finding a stable matching in an instance of SM. We also extend the result for ESM to the SR case. Finally, we study some variants of ESM under weaker forms of exchange-stability, presenting both polynomial-time solvability and NP-completeness results for the corresponding existence questions
Allocation of Heterogeneous Resources of an IoT Device to Flexible Services
Internet of Things (IoT) devices can be equipped with multiple heterogeneous
network interfaces. An overwhelmingly large amount of services may demand some
or all of these interfaces' available resources. Herein, we present a precise
mathematical formulation of assigning services to interfaces with heterogeneous
resources in one or more rounds. For reasonable instance sizes, the presented
formulation produces optimal solutions for this computationally hard problem.
We prove the NP-Completeness of the problem and develop two algorithms to
approximate the optimal solution for big instance sizes. The first algorithm
allocates the most demanding service requirements first, considering the
average cost of interfaces resources. The second one calculates the demanding
resource shares and allocates the most demanding of them first by choosing
randomly among equally demanding shares. Finally, we provide simulation results
giving insight into services splitting over different interfaces for both
cases.Comment: IEEE Internet of Things Journa
Support theorems in abstract settings
In this paper we establish a general framework in which the verification of
support theorems for generalized convex functions acting between an algebraic
structure and an ordered algebraic structure is still possible. As for the
domain space, we allow algebraic structures equipped with families of algebraic
operations whose operations are mutually distributive with respect to each
other. We introduce several new concepts in such algebraic structures, the
notions of convex set, extreme set, and interior point with respect to a given
family of operations, furthermore, we describe their most basic and required
properties. In the context of the range space, we introduce the notion of
completeness of a partially ordered set with respect to the existence of the
infimum of lower bounded chains, we also offer several sufficient condition
which imply this property. For instance, the order generated by a sharp cone in
a vector space turns out to possess this completeness property. By taking
several particular cases, we deduce support and extension theorems in various
classical and important settings
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