# Optimal algorithms for the vertex updating problem of a minimum spanning tree

@article{Johnson1992OptimalAF, title={Optimal algorithms for the vertex updating problem of a minimum spanning tree}, author={Donald B. Johnson and Panagiotis Takis Metaxas}, journal={Proceedings Sixth International Parallel Processing Symposium}, year={1992}, pages={306-314} }

The vertex updating problem for a minimum spanning tree (MST) is defined as follows: Given a graph G=(V,E/sub G/) and its MST T, update T when a new vertex z is introduced along with weighted edges that connect z with the vertices of G. The authors present a set of rules that, together with a valid tree-contraction schedule are used to produce simple optimal parallel algorithms that run in O(log n) parallel time using n/lgn EREW PRAMs where n= mod V mod . These rules can also be used to derive…

## 9 Citations

### Optimal algorithms for the single and multiple vertex updating problems of a minimum spanning tree

- Computer ScienceAlgorithmica
- 2005

A set of rules are presented that produce simple optimal parallel algorithms that run inO(lgn) time usingn/lgn EREW PRAM processors, wheren=¦V¦, and can be used to derive simple linear-time sequential algorithms for the same problem.

### Work-Efficient Batch-Incremental Minimum Spanning Trees with Applications to the Sliding-Window Model

- Computer ScienceSPAA
- 2020

This paper presents the first work-efficient parallel batch-dynamic algorithm for incremental MST, which can insert l edges in O(l log(1+n/l) work in expectation and O(polylog(n) span w.p.h.)), and demonstrates a range of applications that become efficiently solvable in parallel in the sliding-window model.

### Generalised k-Steiner Tree Problems in Normed Planes

- MathematicsAlgorithmica
- 2013

This paper generalises Georgakopoulos and Papadimitriou's approach in order to solve the k-Steiner tree problem, in which the Steiner minimum tree may contain up to k Steiner points for a given constant k, and shows that, for any fixed k, such problems can be solved in O(n2k) time.

### FROM PARALLEL TO SEQUENTIAL : KEEPING OPTIMALITY IN

- Computer Science
- 2007

This paper shows how to design fast (in fact optimal) sequential algorithms from the optimal parallel algorithms for a graph theoretic problem that arizes often in many areas including Economics and Operations Research.

### Parallel Batch-Dynamic Trees via Change Propagation

- Computer ScienceESA
- 2020

This work designs the first work-efficient parallel batch-dynamic algorithm for dynamic trees that is capable of supporting both path queries and subtree queries, as well as a variety of non-local queries.

### Batch-dynamic Algorithms via Parallel Change Propagation and Applications to Dynamic Trees

- Computer ScienceArXiv
- 2020

This paper proposes a framework for algorithmically dynamizing static round-synchronous algorithms to obtain parallel batchdynamic algorithms with good bounds on their work and span, and develops the first work-efficient parallel batch-dynamic algorithm for dynamic trees that supports both subtree queries and path queries.

### General purpose parallel computing

- Computer Science
- 1993

Current issues involved in the development of systems which support ne grain concurrency in a single shared address space are discussed, including algorithmic, architectural, technological, and programming issues.

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