
A Quantum Algorithm for Minimum Steiner Tree Problem
Minimum Steiner tree problem is a wellknown NPhard problem. For the mi...
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Quantum Dynamic Programming Algorithm for DAGs. Applications for ANDOR DAG Evaluation and DAG's Diameter Search
In this paper, we present Quantum Dynamic Programming approach for probl...
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Quantum speedups for dynamic programming on ndimensional lattice graphs
Motivated by the quantum speedup for dynamic programming on the Boolean ...
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Finding Optimal Longest Paths by Dynamic Programming in Parallel
We propose an exact algorithm for solving the longest simple path proble...
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A 1.5Approximation for Path TSP
We present a 1.5approximation for the Metric Path Traveling Salesman Pr...
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A Lattice Linear Predicate Parallel Algorithm for the Dynamic Programming Problems
It has been shown that the parallel Lattice Linear Predicate (LLP) algor...
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Linear time dynamic programming for the exact path of optimal models selected from a finite set
Many learning algorithms are formulated in terms of finding model parame...
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Quantum Speedups for ExponentialTime Dynamic Programming Algorithms
In this paper we study quantum algorithms for NPcomplete problems whose best classical algorithm is an exponential time application of dynamic programming. We introduce the path in the hypercube problem that models many of these dynamic programming algorithms. In this problem we are asked whether there is a path from 0^n to 1^n in a given subgraph of the Boolean hypercube, where the edges are all directed from smaller to larger Hamming weight. We give a quantum algorithm that solves path in the hypercube in time O^*(1.817^n). The technique combines Grover's search with computing a partial dynamic programming table. We use this approach to solve a variety of vertex ordering problems on graphs in the same time O^*(1.817^n), and graph bandwidth in time O^*(2.946^n). Then we use similar ideas to solve the travelling salesman problem and minimum set cover in time O^*(1.728^n).
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