11,041 research outputs found
Finding branch-decompositions of matroids, hypergraphs, and more
Given subspaces of a finite-dimensional vector space over a fixed finite
field , we wish to find a "branch-decomposition" of these subspaces
of width at most , that is a subcubic tree with leaves mapped
bijectively to the subspaces such that for every edge of , the sum of
subspaces associated with leaves in one component of and the sum of
subspaces associated with leaves in the other component have the intersection
of dimension at most . This problem includes the problems of computing
branch-width of -represented matroids, rank-width of graphs,
branch-width of hypergraphs, and carving-width of graphs.
We present a fixed-parameter algorithm to construct such a
branch-decomposition of width at most , if it exists, for input subspaces of
a finite-dimensional vector space over . Our algorithm is analogous
to the algorithm of Bodlaender and Kloks (1996) on tree-width of graphs. To
extend their framework to branch-decompositions of vector spaces, we developed
highly generic tools for branch-decompositions on vector spaces. The only known
previous fixed-parameter algorithm for branch-width of -represented
matroids was due to Hlin\v{e}n\'y and Oum (2008) that runs in time
where is the number of elements of the input -represented
matroid. But their method is highly indirect. Their algorithm uses the
non-trivial fact by Geelen et al. (2003) that the number of forbidden minors is
finite and uses the algorithm of Hlin\v{e}n\'y (2005) on checking monadic
second-order formulas on -represented matroids of small
branch-width. Our result does not depend on such a fact and is completely
self-contained, and yet matches their asymptotic running time for each fixed
.Comment: 73 pages, 10 figure
Classification of the BPS states in Bagger-Lambert Theory
We classify, in a group theoretical manner, the BPS configurations in the
multiple M2-brane theory recently proposed by Bagger and Lambert. We present
three types of BPS equations preserving various fractions of supersymmetries:
in the first type we have constant fields and the interactions are purely
algebraic in nature; in the second type the equations are invariant under
spatial rotation SO(2), and the fields can be time-dependent; in the third
class the equations are invariant under boost SO(1,1) and provide the
eleven-dimensional generalizations of the Nahm equations. The BPS equations for
different number of supersymmetries exhibit the division algebra structures:
octonion, quarternion or complex.Comment: 28+1 pages, No figure; v2 Sec.3.3 slightly expanded, typos fixed; v3
some comments added, to appear in JHE
Development of Navigation Control Algorithm for AGV Using D* Search Algorithm
In this paper, we present a navigation control algorithm for Automatic Guided Vehicles (AGV) that move in industrial environments including static and moving obstacles using D* algorithm. This algorithm has ability to get paths planning in unknown, partially known and changing environments efficiently. To apply the D* search algorithm, the grid map represent the known environment is generated. By using the laser scanner LMS-151 and laser navigation sensor NAV-200, the grid map is updated according to the changing of environment and obstacles. When the AGV finds some new map information such as new unknown obstacles, it adds the information to its map and re-plans a new shortest path from its current coordinates to the given goal coordinates. It repeats the process until it reaches the goal coordinates. This algorithm is verified through simulation and experiment. The simulation and experimental results show that the algorithm can be used to move the AGV successfully to reach the goal position while it avoids unknown moving and static obstacles. [Keywords— navigation control algorithm; Automatic Guided Vehicles (AGV); D* search algorithm
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