13,457 research outputs found
BSA - exact algorithm computing LTS estimate
The main result of this paper is a new exact algorithm computing the estimate
given by the Least Trimmed Squares (LTS). The algorithm works under very weak
assumptions. To prove that, we study the respective objective function using
basic techniques of analysis and linear algebra.Comment: 18 pages, 1 figur
An ETH-Tight Exact Algorithm for Euclidean TSP
We study exact algorithms for {\sc Euclidean TSP} in . In the
early 1990s algorithms with running time were presented for
the planar case, and some years later an algorithm with
running time was presented for any . Despite significant interest in
subexponential exact algorithms over the past decade, there has been no
progress on {\sc Euclidean TSP}, except for a lower bound stating that the
problem admits no algorithm unless ETH fails. Up to
constant factors in the exponent, we settle the complexity of {\sc Euclidean
TSP} by giving a algorithm and by showing that a
algorithm does not exist unless ETH fails.Comment: To appear in FOCS 201
Exact Algorithm for Sampling the 2D Ising Spin Glass
A sampling algorithm is presented that generates spin glass configurations of
the 2D Edwards-Anderson Ising spin glass at finite temperature, with
probabilities proportional to their Boltzmann weights. Such an algorithm
overcomes the slow dynamics of direct simulation and can be used to study
long-range correlation functions and coarse-grained dynamics. The algorithm
uses a correspondence between spin configurations on a regular lattice and
dimer (edge) coverings of a related graph: Wilson's algorithm [D. B. Wilson,
Proc. 8th Symp. Discrete Algorithms 258, (1997)] for sampling dimer coverings
on a planar lattice is adapted to generate samplings for the dimer problem
corresponding to both planar and toroidal spin glass samples. This algorithm is
recursive: it computes probabilities for spins along a "separator" that divides
the sample in half. Given the spins on the separator, sample configurations for
the two separated halves are generated by further division and assignment. The
algorithm is simplified by using Pfaffian elimination, rather than Gaussian
elimination, for sampling dimer configurations. For n spins and given floating
point precision, the algorithm has an asymptotic run-time of O(n^{3/2}); it is
found that the required precision scales as inverse temperature and grows only
slowly with system size. Sample applications and benchmarking results are
presented for samples of size up to n=128^2, with fixed and periodic boundary
conditions.Comment: 18 pages, 10 figures, 1 table; minor clarification
"Exact" Algorithm for Random-Bond Ising Models in 2D
We present an efficient algorithm for calculating the properties of Ising
models in two dimensions, directly in the spin basis, without the need for
mapping to fermion or dimer models. The algorithm gives numerically exact
results for the partition function and correlation functions at a single
temperature on any planar network of N Ising spins in O(N^{3/2}) time or less.
The method can handle continuous or discrete bond disorder and is especially
efficient in the case of bond or site dilution, where it executes in O(L^2 ln
L) time near the percolation threshold. We demonstrate its feasibility on the
ferromagnetic Ising model and the +/- J random-bond Ising model (RBIM) and
discuss the regime of applicability in cases of full frustration such as the
Ising antiferromagnet on a triangular lattice.Comment: 4.2 pages, 5 figures, accepted for publication in Phys. Rev. Let
Exact Algorithm for Graph Homomorphism and Locally Injective Graph Homomorphism
For graphs and , a homomorphism from to is a function , which maps vertices adjacent in to adjacent vertices
of . A homomorphism is locally injective if no two vertices with a common
neighbor are mapped to a single vertex in . Many cases of graph homomorphism
and locally injective graph homomorphism are NP-complete, so there is little
hope to design polynomial-time algorithms for them. In this paper we present an
algorithm for graph homomorphism and locally injective homomorphism working in
time , where is the bandwidth of the
complement of
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