913 research outputs found
Stable Marriage with Multi-Modal Preferences
We introduce a generalized version of the famous Stable Marriage problem, now
based on multi-modal preference lists. The central twist herein is to allow
each agent to rank its potentially matching counterparts based on more than one
"evaluation mode" (e.g., more than one criterion); thus, each agent is equipped
with multiple preference lists, each ranking the counterparts in a possibly
different way. We introduce and study three natural concepts of stability,
investigate their mutual relations and focus on computational complexity
aspects with respect to computing stable matchings in these new scenarios.
Mostly encountering computational hardness (NP-hardness), we can also spot few
islands of tractability and make a surprising connection to the \textsc{Graph
Isomorphism} problem
Local search for stable marriage problems with ties and incomplete lists
The stable marriage problem has a wide variety of practical applications,
ranging from matching resident doctors to hospitals, to matching students to
schools, or more generally to any two-sided market. We consider a useful
variation of the stable marriage problem, where the men and women express their
preferences using a preference list with ties over a subset of the members of
the other sex. Matchings are permitted only with people who appear in these
preference lists. In this setting, we study the problem of finding a stable
matching that marries as many people as possible. Stability is an envy-free
notion: no man and woman who are not married to each other would both prefer
each other to their partners or to being single. This problem is NP-hard. We
tackle this problem using local search, exploiting properties of the problem to
reduce the size of the neighborhood and to make local moves efficiently.
Experimental results show that this approach is able to solve large problems,
quickly returning stable matchings of large and often optimal size.Comment: 12 pages, Proc. PRICAI 2010 (11th Pacific Rim International
Conference on Artificial Intelligence), Byoung-Tak Zhang and Mehmet A. Orgun
eds., Springer LNA
An Exact Algorithm for TSP in Degree-3 Graphs via Circuit Procedure and Amortization on Connectivity Structure
The paper presents an O^*(1.2312^n)-time and polynomial-space algorithm for
the traveling salesman problem in an n-vertex graph with maximum degree 3. This
improves the previous time bounds of O^*(1.251^n) by Iwama and Nakashima and
O^*(1.260^n) by Eppstein. Our algorithm is a simple branch-and-search
algorithm. The only branch rule is designed on a cut-circuit structure of a
graph induced by unprocessed edges. To improve a time bound by a simple
analysis on measure and conquer, we introduce an amortization scheme over the
cut-circuit structure by defining the measure of an instance to be the sum of
not only weights of vertices but also weights of connected components of the
induced graph.Comment: 24 pages and 4 figure
Unbounded-Error Classical and Quantum Communication Complexity
Since the seminal work of Paturi and Simon \cite[FOCS'84 & JCSS'86]{PS86},
the unbounded-error classical communication complexity of a Boolean function
has been studied based on the arrangement of points and hyperplanes. Recently,
\cite[ICALP'07]{INRY07} found that the unbounded-error {\em quantum}
communication complexity in the {\em one-way communication} model can also be
investigated using the arrangement, and showed that it is exactly (without a
difference of even one qubit) half of the classical one-way communication
complexity. In this paper, we extend the arrangement argument to the {\em
two-way} and {\em simultaneous message passing} (SMP) models. As a result, we
show similarly tight bounds of the unbounded-error two-way/one-way/SMP
quantum/classical communication complexities for {\em any} partial/total
Boolean function, implying that all of them are equivalent up to a
multiplicative constant of four. Moreover, the arrangement argument is also
used to show that the gap between {\em weakly} unbounded-error quantum and
classical communication complexities is at most a factor of three.Comment: 11 pages. To appear at Proc. ISAAC 200
The OU-ISIR Gait Database Comprising the Large Population Dataset and Performance Evaluation of Gait Recognition
Transcriptional double-autorepression feedforward circuits act for multicellularity and nervous system development
The Magic Number Problem for Subregular Language Families
We investigate the magic number problem, that is, the question whether there
exists a minimal n-state nondeterministic finite automaton (NFA) whose
equivalent minimal deterministic finite automaton (DFA) has alpha states, for
all n and alpha satisfying n less or equal to alpha less or equal to exp(2,n).
A number alpha not satisfying this condition is called a magic number (for n).
It was shown in [11] that no magic numbers exist for general regular languages,
while in [5] trivial and non-trivial magic numbers for unary regular languages
were identified. We obtain similar results for automata accepting subregular
languages like, for example, combinational languages, star-free, prefix-,
suffix-, and infix-closed languages, and prefix-, suffix-, and infix-free
languages, showing that there are only trivial magic numbers, when they exist.
For finite languages we obtain some partial results showing that certain
numbers are non-magic.Comment: In Proceedings DCFS 2010, arXiv:1008.127
Numerical Simulation of 3D Image Reconstruction of LHD Plasma with IR Imaging Video Bolometers
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