Digital image processing (2nd ed.)
Digital image processing (2nd ed.)
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Numerical stability of geometric algorithms
SCG '87 Proceedings of the third annual symposium on Computational geometry
Verifiable implementation of geometric algorithms using finite precision arithmetic
Artificial Intelligence - Special issue on geometric reasoning
Most uniform path partitioning and its use in image processing
Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
Robust Geometric Computation Based on Topological Consistency
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Convex Embeddings and Bisections of 3-Connected Graphs1
Combinatorica
Operating systems
A plane graph representation of triconnected graphs
Theoretical Computer Science
| Hi-index | 5.23 |
Given two disjoint subsets T1 and T2 of nodes in a 3-connected graph G = (V,E) with a node set V and an arc set E, where |T1| and |T2| are even numbers, it is known that V can be partitioned into two sets V1 and V2 such that the graphs induced by V1 and V2 are both connected and |V1 ∩ Tj| = |V2 ∩ Tj| = |Tj|/2 holds for each j = 1.2. An O(|V|2 log |V|) time and O(|V| + |E|) space algorithm lbr finding such a bipartition has been proposed based on a geometric argument, where G is embedded m the plane R2 and the node set is bipartitioned by a ham-sandwich cut on the embedding. A naive implementation of the algorithm, however, requires high precision real arithmetic to distinguish two close points in a large set of points on R2. In this paper, we propose an O(|V|2) time and space algorithm to the problem. The new algorithm, which remains to be based on the geometric embedding, can construct a solution purely combinatorially in the sense that it does not require computing actual embedded points in R2 and thereby no longer needs to store any real number for embedded points. Although the new algorithm seems to need more space complexity, it can be implemented only with |V| linked lists such that each element stores an integer in [1,|V|].