228,543 research outputs found
Teichm\"uller polynomials of fibered alternating links
We give an algorithm for computing the Teichm\"uller polynomial for a certain
class of fibered alternating links associated to trees. Furthermore, we exhibit
a mutant pair of such links distinguished by the Teichm\"uller polynomial.Comment: 22 pages, 12 figure
Computing on Anonymous Quantum Network
This paper considers distributed computing on an anonymous quantum network, a
network in which no party has a unique identifier and quantum communication and
computation are available. It is proved that the leader election problem can
exactly (i.e., without error in bounded time) be solved with at most the same
complexity up to a constant factor as that of exactly computing symmetric
functions (without intermediate measurements for a distributed and superposed
input), if the number of parties is given to every party. A corollary of this
result is a more efficient quantum leader election algorithm than existing
ones: the new quantum algorithm runs in O(n) rounds with bit complexity
O(mn^2), on an anonymous quantum network with n parties and m communication
links. Another corollary is the first quantum algorithm that exactly computes
any computable Boolean function with round complexity O(n) and with smaller bit
complexity than that of existing classical algorithms in the worst case over
all (computable) Boolean functions and network topologies. More generally, any
n-qubit state can be shared with that complexity on an anonymous quantum
network with n parties.Comment: 25 page
Software-based fault-tolerant routing algorithm in multidimensional networks
Massively parallel computing systems are being built with hundreds or thousands of components such as nodes, links, memories, and connectors. The failure of a component in such systems will not only reduce the computational power but also alter the network's topology. The software-based fault-tolerant routing algorithm is a popular routing to achieve fault-tolerance capability in networks. This algorithm is initially proposed only for two dimensional networks (Suh et al., 2000). Since, higher dimensional networks have been widely employed in many contemporary massively parallel systems; this paper proposes an approach to extend this routing scheme to these indispensable higher dimensional networks. Deadlock and livelock freedom and the performance of presented algorithm, have been investigated for networks with different dimensionality and various fault regions. Furthermore, performance results have been presented through simulation experiments
-minimization method for link flow correction
A computational method, based on -minimization, is proposed for the
problem of link flow correction, when the available traffic flow data on many
links in a road network are inconsistent with respect to the flow conservation
law. Without extra information, the problem is generally ill-posed when a large
portion of the link sensors are unhealthy. It is possible, however, to correct
the corrupted link flows \textit{accurately} with the proposed method under a
recoverability condition if there are only a few bad sensors which are located
at certain links. We analytically identify the links that are robust to
miscounts and relate them to the geometric structure of the traffic network by
introducing the recoverability concept and an algorithm for computing it. The
recoverability condition for corrupted links is simply the associated
recoverability being greater than 1. In a more realistic setting, besides the
unhealthy link sensors, small measurement noises may be present at the other
sensors. Under the same recoverability condition, our method guarantees to give
an estimated traffic flow fairly close to the ground-truth data and leads to a
bound for the correction error. Both synthetic and real-world examples are
provided to demonstrate the effectiveness of the proposed method
The HOMFLY-PT Polynomial is Fixed-Parameter Tractable
Many polynomial invariants of knots and links, including the Jones and HOMFLY-PT polynomials, are widely used in practice but #P-hard to compute. It was shown by Makowsky in 2001 that computing the Jones polynomial is fixed-parameter tractable in the treewidth of the link diagram, but the parameterised complexity of the more powerful HOMFLY-PT polynomial remained an open problem. Here we show that computing HOMFLY-PT is fixed-parameter tractable in the treewidth, and we give the first sub-exponential time algorithm to compute it for arbitrary links
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