
Consistent recovery threshold of hidden nearest neighbor graphs
Motivated by applications such as discovering strong ties in social netw...
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Feedback Vertex Set on Hamiltonian Graphs
We study the computational complexity of Feedback Vertex Set on subclass...
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A new constraint of the Hamilton cycle algorithm
Grinberg's theorem is a necessary condition for the planar Hamilton grap...
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A Method to Compute the Sparse Graphs for Traveling Salesman Problem Based on Frequency Quadrilaterals
In this paper, an iterative algorithm is designed to compute the sparse ...
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Largedeviation Properties of Linearprogramming Computational Hardness of the Vertex Cover Problem
The distribution of the computational cost of linearprogramming (LP) re...
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Bayesian Metabolic Flux Analysis reveals intracellular flux couplings
Metabolic flux balance analyses are a standard tool in analysing metabol...
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Hidden Hamiltonian Cycle Recovery via Linear Programming
We introduce the problem of hidden Hamiltonian cycle recovery, where there is an unknown Hamiltonian cycle in an nvertex complete graph that needs to be inferred from noisy edge measurements. The measurements are independent and distributed according to _n for edges in the cycle and _n otherwise. This formulation is motivated by a problem in genome assembly, where the goal is to order a set of contigs (genome subsequences) according to their positions on the genome using longrange linking measurements between the contigs. Computing the maximum likelihood estimate in this model reduces to a Traveling Salesman Problem (TSP). Despite the NPhardness of TSP, we show that a simple linear programming (LP) relaxation, namely the fractional 2factor (F2F) LP, recovers the hidden Hamiltonian cycle with high probability as n →∞ provided that α_n  n →∞, where α_n 2 ∫√(d P_n d Q_n) is the Rényi divergence of order 1/2. This condition is informationtheoretically optimal in the sense that, under mild distributional assumptions, α_n ≥ (1+o(1)) n is necessary for any algorithm to succeed regardless of the computational cost. Departing from the usual proof techniques based on dual witness construction, the analysis relies on the combinatorial characterization (in particular, the halfintegrality) of the extreme points of the F2F polytope. Represented as bicolored multigraphs, these extreme points are further decomposed into simpler "blossomtype" structures for the large deviation analysis and counting arguments. Evaluation of the algorithm on real data shows improvements over existing approaches.
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