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Traveling Salesman Path problems
, 2005
"... In the traveling salesman path problem, we are given a set of cities, traveling costs between city pairs and fixed source and destination cities. The objective is to find a minimum cost path from the source to destination visiting all cities exactly once. In this paper, we study polyhedral and combi ..."
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Cited by 12 (0 self)
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In the traveling salesman path problem, we are given a set of cities, traveling costs between city pairs and fixed source and destination cities. The objective is to find a minimum cost path from the source to destination visiting all cities exactly once. In this paper, we study polyhedral
On the LP relaxation of the asymmetric traveling salesman path problem
 Theory of Computing
, 2008
"... Abstract: This is a comment on the article “An O(logn) Approximation Ratio for the ..."
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Abstract: This is a comment on the article “An O(logn) Approximation Ratio for the
An O(log n) Approximation Ratio for the Asymmetric Traveling Salesman Path Problem
 THEORY OF COMPUTING
, 2007
"... We consider a variant of the traveling salesman problem (TSP): Given a directed graph G = (V,A) with nonnegative arc lengths ℓ: A → R + and a pair of vertices s,t, find an st walk of minimum length that visits all the vertices in V. If ℓ satisfies the asymmetric triangle inequality, the problem i ..."
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Cited by 13 (0 self)
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is equivalent to that of finding an st path of minimum length that visits all the vertices. We refer to this problem as the asymmetric traveling salesman path problem (ATSPP). When s = t this is the well known asymmetric traveling salesman tour problem (ATSP). Although an O(logn) approximation ratio has long
The AnKleinbergShmoys Algorithm for the Traveling Salesman Path Problem ∗
"... We will assume throughout that we are given a complete undirected graph G = (V, E) with edge costs c: E → R≥0 and that these edge costs satisfy the Triangle Inequality (c(u, w) ≤ c(u, v) + c(v, w) for all u, v, w ∈ V). The shortest path costs in this graph are then a metric. Recall that a Hamiltoni ..."
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Hamiltonian cycle is a cycle than includes each vertex exactly once and a Hamiltonian path is a path that visits each vertex exactly once. Now, we define the traveling salesman problem and a couple of its variants Traveling Salesman Problem (TSP) Find the cheapest Hamiltonian cycle. Traveling Salesman Path
LPbased approximation algorithms for traveling salesman path problems. arXiv manuscript number 1105.2391
"... ar ..."
Ant Colony System: A cooperative learning approach to the traveling salesman problem
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
, 1997
"... This paper introduces the ant colony system (ACS), a distributed algorithm that is applied to the traveling salesman problem (TSP). In the ACS, a set of cooperating agents called ants cooperate to find good solutions to TSP’s. Ants cooperate using an indirect form of communication mediated by a pher ..."
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Cited by 1000 (53 self)
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This paper introduces the ant colony system (ACS), a distributed algorithm that is applied to the traveling salesman problem (TSP). In the ACS, a set of cooperating agents called ants cooperate to find good solutions to TSP’s. Ants cooperate using an indirect form of communication mediated by a
− ɛapproximation Algorithm for TSPP Part 2 ∗ This is a continuation of the previous lecture describing the AnKleinbergShmoys algorithm for the Traveling Salesman Path Problem [AKS11].
"... We begin by reviewing notes and definitions from the previous lecture. First, we give an LP relaxation for TSPP: min c(x): = ∑ e∈E cexe s.t. x(∂S) ≥ 1 for separating cuts, i.e. S ∩ {s, t}  = 1, with S > 1 x(∂S) ≥ 2 for nonseparating cuts with S > 1 x(∂S) = 2 for cuts with S  = 1 ..."
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needs to be fixed. As described above, T  is even. 5. Take M to be the minimum cost matching on T. 6. Then A ∪ M has an Eulerian path from s to t. Shortcut to avoid taking the same edge twice and return the resulting path. We will make heavy use of two other properties in this lecture: 1. Fractional T
Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 681 (1 self)
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It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard
Regularization paths for generalized linear models via coordinate descent
, 2009
"... We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, twoclass logistic regression, and multinomial regression problems while the penalties include ℓ1 (the lasso), ℓ2 (ridge regression) and mixtures of the two (the elastic ..."
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Cited by 698 (14 self)
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elastic net). The algorithms use cyclical coordinate descent, computed along a regularization path. The methods can handle large problems and can also deal efficiently with sparse features. In comparative timings we find that the new algorithms are considerably faster than competing methods.
Molecular Computation Of Solutions To Combinatorial Problems
, 1994
"... The tools of molecular biology are used to solve an instance of the directed Hamiltonian path problem. A small graph is encoded in molecules of DNA and the `operations' of the computation are performed with standard protocols and enzymes. This experiment demonstrates the feasibility of carrying ..."
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Cited by 766 (6 self)
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The tools of molecular biology are used to solve an instance of the directed Hamiltonian path problem. A small graph is encoded in molecules of DNA and the `operations' of the computation are performed with standard protocols and enzymes. This experiment demonstrates the feasibility
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