• Corpus ID: 226278344

Vertex Fault-Tolerant Geometric Spanners for Weighted Points

  title={Vertex Fault-Tolerant Geometric Spanners for Weighted Points},
  author={Sukanya Bhattacharjee and Rajasekhar Inkulu},
Given a set S of n points, a weight function w to associate a non-negative weight to each point in S, a positive integer k \ge 1, and a real number \epsilon > 0, we present algorithms for computing a spanner network G(S, E) for the metric space (S, d_w) induced by the weighted points in S. The weighted distance function d_w on the set S of points is defined as follows: for any p, q \in S, d_w(p, q) is equal to w(p) + d_\pi(p, q) + w(q) if p \ne q, otherwise, d_w(p, q) is 0. Here, d_\pi(p, q) is… 



Fault-Tolerant Additive Weighted Geometric Spanners

The additive weighted distance d_w(p,q) between two points p,q belonging to S is defined as w(p) + d( p, q) + w(q) if p \ne q and it is zero if p = q, where p is a real number and q is a integer.

Improved Algorithms for Constructing Fault-Tolerant Spanners

Algorithms are given that construct k -fault-tolerant spanners for S, a set of n points in a metric space, whose total edge length is O(ck) times the weight of a minimum spanning tree of S, for some constant c .

Dynamic algorithms for geometric spanners of small diameter: Randomized solutions

An optimal algorithm for computing angle-constrained spanners

It is shown that, for any θ with 0 < θ < π/3, a θ-angle-constrained t-spanner can be computed in O(n logn) time, where t depends only on θ.

Geometric Spanners for Weighted Point Sets

This bound on the stretch factor is nearly optimal: in any finite metric space and for any ε>0, it is possible to assign weights to the elements such that any non-complete graph has stretch factor larger than 2−ε.

Spanners of Additively Weighted Point Sets

Fast Greedy Algorithms for Constructing Sparse Geometric Spanners

The first O(nlog n)-time algorithm to compute a geometric t-spanner on V, a connected graph G = (V,E) with edge weights equal to the Euclidean distances between the endpoints, and its degree is bounded by a constant.

New Results of Fault Tolerant Geometric Spanners

A construction of a k-vertex fault tolerant spanner with O(kn) edges which is a tight bound and a more natural but stronger definition of k-edge fault tolerance which not necessarily can be satisfied if one allows only simple edges between the points of S.

Randomized and deterministic algorithms for geometric spanners of small diameter

  • S. AryaD. MountM. Smid
  • Mathematics, Computer Science
    Proceedings 35th Annual Symposium on Foundations of Computer Science
  • 1994
Randomized and deterministic algorithms are given for constructing t-spanners consisting of O(n) edges and having O(log n) diameter and it is shown how to maintain the randomized t-spanner under random insertions and deletions.

On Plane Constrained Bounded-Degree Spanners

The constrained half-θ6-graph (which is identical to the constrained Delaunay graph whose empty visible region is an equilateral triangle) is a plane 2-spanner of Vis(P,S) with maximum degree 6 + c, where c is the maximum number of segments adjacent to a vertex.