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73
Link length of rectilinear Hamiltonian tours
 in grids, Ars Combinatoria
, 1994
"... The link length of a walk in a multidimensional grid is the number of straight line segments constituting the walk. Alternatively, it is the number of turns that a mobile unit needs to perform in traversing the walk. A rectilinear walk consists of straight line segments which are parallel to the mai ..."
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Cited by 10 (0 self)
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The link length of a walk in a multidimensional grid is the number of straight line segments constituting the walk. Alternatively, it is the number of turns that a mobile unit needs to perform in traversing the walk. A rectilinear walk consists of straight line segments which are parallel to the main axis. We wish to construct rectilinear walks with minimal link length traversing grids. If G denotes the multidimensional grid, let s(G) be the minimal link length of a rectilinear walk traversing all the vertices of G. In this paper we develop an asymptotically optimal algorithm for constructing rectilinear walks traversing all the vertices of complete multidimensional grids and analyze the worstcase behavior of s(G), when G is a multidimensional grid.
The knowledge complexity of interactive proof systems

, 1989
"... Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/nonHamiltonian. In th ..."
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Cited by 1246 (39 self)
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Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/nonHamiltonian
Relaxed Tours and Path Ejections for the Traveling Salesman Problem
, 1996
"... We describe an edge based ejection chain method to generate compound neighborhood structures for the Traveling Salesman Problem. These neighborhood structures enclose a special substructure which is not necessarily a Hamiltonian tour. Instead the neighborhood components are linked together to compos ..."
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Cited by 34 (12 self)
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We describe an edge based ejection chain method to generate compound neighborhood structures for the Traveling Salesman Problem. These neighborhood structures enclose a special substructure which is not necessarily a Hamiltonian tour. Instead the neighborhood components are linked together
TSP tours in cubic graphs: Beyond 4/3
, 2015
"... After a sequence of improvements Boyd et al. [TSP on cubic and subcubic graphs, Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 6655, Springer, Heidelberg, 2011, pp. 65–77] proved that any 2connected graph whose n vertices have degree 3, i.e., a cubic 2connected ..."
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Cited by 3 (0 self)
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graph, has a Hamiltonian tour of length at most (4/3)n, establishing in particular that the integrality gap of the subtour LP is at most 4/3 for cubic 2connected graphs and matching the conjectured value of the famous 4/3 conjecture. In this paper we improve upon this result by designing an algorithm
HAMILTONICITY AND THE 3OPT PROCEDURE FOR THE TRAVELING SALESMAN PROBLEM
, 1994
"... The 3Opt procedure deals with interchanging three edges of a tour with three edges not on that tour. For n ≥ 6, the 3Interchange Graph is a graph on 1 2 (n − 1)! vertices, corresponding to the hamiltonian tours in Kn; two vertices are adjacent iff the corresponding hamiltonian tours differ in an ..."
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The 3Opt procedure deals with interchanging three edges of a tour with three edges not on that tour. For n ≥ 6, the 3Interchange Graph is a graph on 1 2 (n − 1)! vertices, corresponding to the hamiltonian tours in Kn; two vertices are adjacent iff the corresponding hamiltonian tours differ
Figurative Tours and Braids
"... We start with a rectangular grid of points, and we connect pairs of points to form either a tour (a Hamiltonian cycle) or a braid (a collection of disjoint paths that start in the top row and end on the bottom). In each case, our goal is to design a graph that will closely resemble a grayscale targe ..."
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We start with a rectangular grid of points, and we connect pairs of points to form either a tour (a Hamiltonian cycle) or a braid (a collection of disjoint paths that start in the top row and end on the bottom). In each case, our goal is to design a graph that will closely resemble a grayscale
Comparison of Heuristics for the Colorful Traveling Salesman Problem
"... In the Colorful Traveling Salesman Problem (CTSP), given a graph G with a (not necessarily distinct) label (color) assigned to each edge, a Hamiltonian tour with the minimum number of different labels is sought. The problem is a variant of the wellknown Hamiltonian Cycle problem and has potential a ..."
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In the Colorful Traveling Salesman Problem (CTSP), given a graph G with a (not necessarily distinct) label (color) assigned to each edge, a Hamiltonian tour with the minimum number of different labels is sought. The problem is a variant of the wellknown Hamiltonian Cycle problem and has potential
Université de Tours F37 200 TOURS (France)
, 2008
"... The main result of Xiao et al. [ Phys. Rev. Lett. 95, 137204 (2005)] follows from Hamiltonian mechanics. In a recent paper on the semiclassical dynamics of a Bloch electron, Xiao, Shi and Niu [1] claim that, due to a Berry curvature term, Liouville’s theorem on the conservation of the phasespace vol ..."
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The main result of Xiao et al. [ Phys. Rev. Lett. 95, 137204 (2005)] follows from Hamiltonian mechanics. In a recent paper on the semiclassical dynamics of a Bloch electron, Xiao, Shi and Niu [1] claim that, due to a Berry curvature term, Liouville’s theorem on the conservation of the phasespace
2008a), “Pairwise Display of highdimensional information via Eulerian tours and Hamiltonian decompositions
, 1975
"... A graph theoretic approach is taken to the component order problem in the layout of statistical graphics. Eulerian tours and Hamiltonian decompositions of complete graphs are used to ameliorate order effects in statistical graphics. Similar traversals of edge weighted graphs are used to amplify the ..."
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Cited by 9 (1 self)
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A graph theoretic approach is taken to the component order problem in the layout of statistical graphics. Eulerian tours and Hamiltonian decompositions of complete graphs are used to ameliorate order effects in statistical graphics. Similar traversals of edge weighted graphs are used to amplify
Results 1  10
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73