Monotone Paths in Line Arrangements with a Small Number of Directions
نویسندگان
چکیده
منابع مشابه
Monotone Paths in Line Arrangements with a Small Number of Directions
We give subquadratic bounds on the maximum length of an x-monotone path in an arrangement of n lines with at most C log logn directions, where C is a suitable constant. For instance, the maximum length of an x-monotone path in an arrangement of n lines having at most ten slopes is O(n67=34). In particular, we get tight estimates for the case of lines having at most five directions, by showing t...
متن کاملOn shortest paths in line arrangements
In this paper, we show that the shortest path between two points in a grid-like arrangement of two pencils of lines has a particularly simple structure, as was previously conjectured. This gives a linear-time algorithm for computing shortest paths in such arrangements.
متن کاملOn some monotone path problems in line arrangements
Consider a set of lines in the plane. The lines of induce a cell complex, ! " $# , called the arrangement of , whose vertices are the intersection points of the lines, whose edges are the maximal portions of lines containing no vertices and whose two-dimensional cells are the connected components of %'&)('*,+.-0/ 1 . It is assumed that none of the lines is parallel to the 2 -axis. One of the pr...
متن کاملThe saturation number for the length of degree monotone paths
A degree monotone path in a graph G is a path P such that the sequence of degrees of the vertices in the order in which they appear on P is monotonic. The length (number of vertices) of the longest degree monotone path in G is denoted by mp(G). This parameter, inspired by the well-known ErdősSzekeres theorem, has been studied by the authors in two earlier papers. Here we consider a saturation p...
متن کاملMonotone Paths in Random Hypergraphs
We determine the probability thresholds for the existence of monotone paths, of finite and infinite length, in random oriented graphs with vertex set N, the set of all increasing k-tuples in N. These graphs appear as line graph of uniform hypergraphs with vertex set N.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2004
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-004-1106-6