269 research outputs found
A branch-and-price algorithm for a hierarchical crew scheduling problem.
We describe a real-life problem arising at a crane rental company. This problem is a generalization of the basic crew scheduling problem given in Mingozzi et al. and Beasley and Cao. We formulate the problem as an integer programming problem and establish ties with the integer multicommodity flow problem and the hierarchical interval scheduling problem. After establishing the complexity of the problem we propose a branch-and-price algorithm to solve it. We test this algorithm on a limited number of real-life instances.Scheduling;
Polychromatic Coloring for Half-Planes
We prove that for every integer , every finite set of points in the plane
can be -colored so that every half-plane that contains at least
points, also contains at least one point from every color class. We also show
that the bound is best possible. This improves the best previously known
lower and upper bounds of and respectively. We also show
that every finite set of half-planes can be colored so that if a point
belongs to a subset of at least of the half-planes then
contains a half-plane from every color class. This improves the best previously
known upper bound of . Another corollary of our first result is a new
proof of the existence of small size \eps-nets for points in the plane with
respect to half-planes.Comment: 11 pages, 5 figure
Linearizable special cases of the QAP
We consider special cases of the quadratic assignment problem (QAP) that are linearizable in the sense of Bookhold. We provide combinatorial characterizations of the linearizable instances of the weighted feedback arc set QAP, and of the linearizable instances of the traveling salesman QAP. As a by-product, this yields a new well-solvable special case of the weighted feedback arc set problem
New special cases of the quadratic assignment problem with diagonally structured coefficient matrices
We consider new polynomially solvable cases of the well-known Quadratic Assignment Problem involving coefficient matrices with a special diagonal structure. By combining the new special cases with polynomially solvable special cases known in the literature we obtain a new and larger class of polynomially solvable special cases of the QAP where one of the two coefficient matrices involved is a Robinson matrix with an additional structural property: this matrix can be represented as a conic combination of cut matrices in a certain normal form. The other matrix is a conic combination of a monotone anti-Monge matrix and a down-benevolent Toeplitz matrix. We consider the recognition problem for the special class of Robinson matrices mentioned above and show that it can be solved in polynomial time
Graph editing to a given degree sequence
We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence where the aim is to obtain a graph with a given degree sequence ÏÏ by at most k vertex or edge deletions and edge additions. We show that the problem is W[1]-hard when parameterized by k for any combination of the allowed editing operations. From the positive side, we show that the problem can be solved in time 2O(k(Î+k)2)n2logn2O(k(Î+k)2)n2logâĄn for n-vertex graphs, where Î=maxÏÎ=maxÏ, i.e., the problem is FPT when parameterized by k+Îk+Î. We also show that Editing to a Graph with a Given Degree Sequence has a polynomial kernel when parameterized by k+Îk+Î if only edge additions are allowed, and there is no polynomial kernel unless NPâcoNP/polyNPâcoNP/poly for all other combinations of allowed editing operations
Universal quantum computation by discontinuous quantum walk
Quantum walks are the quantum-mechanical analog of random walks, in which a
quantum `walker' evolves between initial and final states by traversing the
edges of a graph, either in discrete steps from node to node or via continuous
evolution under the Hamiltonian furnished by the adjacency matrix of the graph.
We present a hybrid scheme for universal quantum computation in which a quantum
walker takes discrete steps of continuous evolution. This `discontinuous'
quantum walk employs perfect quantum state transfer between two nodes of
specific subgraphs chosen to implement a universal gate set, thereby ensuring
unitary evolution without requiring the introduction of an ancillary coin
space. The run time is linear in the number of simulated qubits and gates. The
scheme allows multiple runs of the algorithm to be executed almost
simultaneously by starting walkers one timestep apart.Comment: 7 pages, revte
Polygons with inscribed circles and prescribed side lengths
AbstractWe prove NP-completeness of the following problem: For n given input numbers, decide whether there exists an n-sided, plane, convex polygon that has an inscribed circle and that has the input numbers as side lengths
Electric-dipole active two-magnon excitation in {\textit{ab}} spiral spin phase of a ferroelectric magnet GdTbMnO
A broad continuum-like spin excitation (1--10 meV) with a peak structure
around 2.4 meV has been observed in the ferroelectric spiral spin phase of
GdTbMnO by using terahertz (THz) time-domain spectroscopy.
Based on a complete set of light-polarization measurements, we identify the
spin excitation active for the light vector only along the a-axis, which
grows in intensity with lowering temperature even from above the magnetic
ordering temperature but disappears upon the transition to the -type
antiferromagnetic phase. Such an electric-dipole active spin excitation as
observed at THz frequencies can be ascribed to the two-magnon excitation in
terms of the unique polarization selection rule in a variety of the
magnetically ordered phases.Comment: 11 pages including 3 figure
Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis
Obtaining lower bounds for NP-hard problems has for a long time been an
active area of research. Recent algebraic techniques introduced by Jonsson et
al. (SODA 2013) show that the time complexity of the parameterized SAT()
problem correlates to the lattice of strong partial clones. With this ordering
they isolated a relation such that SAT() can be solved at least as fast
as any other NP-hard SAT() problem. In this paper we extend this method
and show that such languages also exist for the max ones problem
(MaxOnes()) and the Boolean valued constraint satisfaction problem over
finite-valued constraint languages (VCSP()). With the help of these
languages we relate MaxOnes and VCSP to the exponential time hypothesis in
several different ways.Comment: This is an extended version of Relating the Time Complexity of
Optimization Problems in Light of the Exponential-Time Hypothesis, appearing
in Proceedings of the 39th International Symposium on Mathematical
Foundations of Computer Science MFCS 2014 Budapest, August 25-29, 201
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