3,122 research outputs found
Election Attacks with Few Candidates
We investigate the parameterized complexity of strategic behaviors in
generalized scoring rules. In particular, we prove that the manipulation,
control (all the 22 standard types), and bribery problems are fixed-parameter
tractable for most of the generalized scoring rules, with respect to the number
of candidates. Our results imply that all these strategic voting problems are
fixed-parameter tractable for most of the common voting rules, such as
Plurality, r-Approval, Borda, Copeland, Maximin, Bucklin, etc., with respect to
the number of candidates
Approval Voting with Intransitive Preferences
We extend Approval voting to the settings where voters may have intransitive
preferences. The major obstacle to applying Approval voting in these settings
is that voters are not able to clearly determine who they should approve or
disapprove, due to the intransitivity of their preferences. An approach to
address this issue is to apply tournament solutions to help voters make the
decision. We study a class of voting systems where first each voter casts a
vote defined as a tournament, then a well-defined tournament solution is
applied to select the candidates who are assumed to be approved by the voter.
Winners are the ones receiving the most approvals. We study axiomatic
properties of this class of voting systems and complexity of control and
bribery problems for these voting systems.Comment: 11 pages, 1 figure, extended abstract accepted at AAMAS 201
Recognizing Linked Domain in Polynomial Time
The celebrated Gibbard-Satterthwaite Theorem states that any surjective
social choice function which is defined over the universal domain of
preferences and is strategy-proof must be dictatorial. Aswal, Chatterji and Sen
generalize the Gibbard-Satterthwaite theorem by showing that the
Gibbard-Satterthwaite theorem still holds if the universal domain is replaced
with the linked domain. In this note, we show that determining whether an
election is linked can be done in polynomial time.Comment: 2 page
Clustering by Hierarchical Nearest Neighbor Descent (H-NND)
Previously in 2014, we proposed the Nearest Descent (ND) method, capable of
generating an efficient Graph, called the in-tree (IT). Due to some beautiful
and effective features, this IT structure proves well suited for data
clustering. Although there exist some redundant edges in IT, they usually have
salient features and thus it is not hard to remove them.
Subsequently, in order to prevent the seemingly redundant edges from
occurring, we proposed the Nearest Neighbor Descent (NND) by adding the
"Neighborhood" constraint on ND. Consequently, clusters automatically emerged,
without the additional requirement of removing the redundant edges. However,
NND proved still not perfect, since it brought in a new yet worse problem, the
"over-partitioning" problem.
Now, in this paper, we propose a method, called the Hierarchical Nearest
Neighbor Descent (H-NND), which overcomes the over-partitioning problem of NND
via using the hierarchical strategy. Specifically, H-NND uses ND to effectively
merge the over-segmented sub-graphs or clusters that NND produces. Like ND,
H-NND also generates the IT structure, in which the redundant edges once again
appear. This seemingly comes back to the situation that ND faces. However,
compared with ND, the redundant edges in the IT structure generated by H-NND
generally become more salient, thus being much easier and more reliable to be
identified even by the simplest edge-removing method which takes the edge
length as the only measure. In other words, the IT structure constructed by
H-NND becomes more fitted for data clustering. We prove this on several
clustering datasets of varying shapes, dimensions and attributes. Besides,
compared with ND, H-NND generally takes less computation time to construct the
IT data structure for the input data.Comment: 19 pages, 9 figure
Central extensions of generalized orthosymplectic Lie superalgebras
The key ingredient of this paper is the universal central extension of the
generalized orthosymplectic Lie superalgebra
coordinatized by a unital associative superalgebra with
superinvolution. Such a universal central extension will be constructed via a
Steinberg orthosymplectic Lie superalgebra coordinated by . The
research on the universal central extension of
will yield an identification between the second homology group of the
generalized orthosymplectic Lie superalgebra
and the first -graded skew-dihedral homology group of
for . The universal central extensions of
and will also be
treated separately.Comment: The decomposition of given after the
proof of Proposition 3.2 has been revised. Accordingly, the decomposition of
in Proposition 3.6 and 4.1 has been revised.
A few typos have been fixe
Clustering by Descending to the Nearest Neighbor in the Delaunay Graph Space
In our previous works, we proposed a physically-inspired rule to organize the
data points into an in-tree (IT) structure, in which some undesired edges are
allowed to occur. By removing those undesired or redundant edges, this IT
structure is divided into several separate parts, each representing one
cluster. In this work, we seek to prevent the undesired edges from arising at
the source. Before using the physically-inspired rule, data points are at first
organized into a proximity graph which restricts each point to select the
optimal directed neighbor just among its neighbors. Consequently, separated
in-trees or clusters automatically arise, without redundant edges requiring to
be removed.Comment: 7 page
Nonparametric Nearest Neighbor Descent Clustering based on Delaunay Triangulation
In our physically inspired in-tree (IT) based clustering algorithm and the
series after it, there is only one free parameter involved in computing the
potential value of each point. In this work, based on the Delaunay
Triangulation or its dual Voronoi tessellation, we propose a nonparametric
process to compute potential values by the local information. This computation,
though nonparametric, is relatively very rough, and consequently, many local
extreme points will be generated. However, unlike those gradient-based methods,
our IT-based methods are generally insensitive to those local extremes. This
positively demonstrates the superiority of these parametric (previous) and
nonparametric (in this work) IT-based methods.Comment: 7 pages; 6 figure
Trace and inverse trace of Steklov eigenvalues II
This is a continuation of our previous work arXiv:1601.05617 on trace and
inverse trace of Steklov eigenvalues. More new inequalities for the trace and
inverse trace of Steklov eigenvalues are obtained.Comment: The introduction was refine
Howe Duality for Quantum Queer Superalgebras
We establish a new Howe duality between a pair of quantum queer superalgebras
. The key
ingredient is the construction of a non-commutative analogue
of the symmetric superalgebra
with the use of quantum coordinate queer superalgebra.
It turns out that this superalgebra is equipped with a
-supermodule
structure that admits a multiplicity-free decomposition. We also show that the
-Howe
duality implies the Sergeev-Olshanski duality
Trace and inverse trace of Steklov eigenvalues
In this paper, we obtain some new estimates for the trace and inverse trace
of Steklov eigenvalues. The estimates generalize some previous results of
Hersch-Payne-Schiffer , Brock}, Raulot-Savo and Dittmar.Comment: Minor typos correcte
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