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… 

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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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.

Parallel Dynamic Algorithms for MinimumSpanning Trees

References

SHOWING 1-10 OF 25 REFERENCES

Algorithms for Updating Minimal Spanning Trees

An O(log n) Algorithm for Parallel Update of Minimum Spanning Trees

A Parallel Vertex Insertion Algorithm For Minimum Spanning Trees

TLDR
A new parallel algorithm for updating the minimum spanning tree of an n-vertex graph following the addition of a new vertex is presented and is superior to known results on this model.

On Finding and Updating Spanning Trees and Shortest Paths

TLDR
The most notable result is that a spanning tree solution can be updated in $O(n)$ when a new node is added to an n-node graph whose minimum spanning tree is known.

Optimal Tree Contraction in the EREW Model

TLDR
A deterministic parallel algorithm for parallel tree contraction that is optimal in the sense that the product P · T is equal to the input size and gives an O(log n) time algorithm when P = n/log n.

Approximate and exact parallel scheduling with applications to list, tree and graph problems

  • R. ColeU. Vishkin
  • Computer Science
    27th Annual Symposium on Foundations of Computer Science (sfcs 1986)
  • 1986
TLDR
A novel scheduling problem is defined; it is solved by repeated, rapid, approximate reschedulings, which leads to a first optimal PRAM algorithm for list ranking, which runs in logarithmic time.

Efficient parallel algorithms for some graph problems

TLDR
A general time bound is derived for a parallel algorithm that uses K processors for finding the connected components of an undirected graph and the result is optimal in the sense that the speedup ratio is linear with the number of processors used.

An Optimal Parallel Algorithm for Dynamic Expression Evaluation and Its Applications

We describe a deterministic parallel algorithm to compute algebraic expressions in log n time using n/log(n) processors on a parallel random access machine without write conflicts (P-RAM) with no

Parallel tree contraction and its application

  • G. MillerJ. Reif
  • Computer Science
    26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
  • 1985
TLDR
A bottom-up algorithm to handle trees which has two major advantages over the top-down approach: the control structure is straight forward and easier to implement facilitating new algorithms using fewer processors and less time; and problems for which it was too difficult or too complicated to find polylog parallel algorithms are now easy.

Optimal Parallel Evaluation of Tree-Structured Computations by Raking

TLDR
The algorithm can be viewed as avoiding COMPRESSes entirely and simply performing RAKEs and can be modified easily to evaluate every subexpression of the original arithmetic expression.