Multithreaded Clustering for Multi-level Hypergraph Partitioning

Q: What is the reason why the thread recomputes the total weight of vr?

it recomputes the total weight of u and vr (line 3) since new vertices might have been inserted to vr’s cluster by other threads.

Question

1. What have the authors contributed in "Multithreaded clustering for multi-level hypergraph partitioning" ?

2. What is the way to find the speedups on the overall execution time?

3. What is the time consuming part of the current-state-of-the-art?

4. What is the function of the array conn?

Accepted Answer

The current-state-of-the art software libraries that provide tool support for the hypergraph partitioning problem are designed and implemented before the game-changing advancements in multi-core computing.. In this approach, a given hypergraph is coarsened to a much smaller one, a partition is obtained on the the smallest hypergraph, and that partition is projected to the original hypergraph while refining it on the intermediate hypergraphs.. The authors present three efficient multithreaded clustering algorithms which are very suited for multi-level partitioners.. The authors compare their performance with that of the ones currently used in today ’ s hypergraph partitioners.. The authors show on a large number of real life hypergraphs that their implementations, integrated into a commonly used partitioning library PaToH, achieve good speedups without reducing the clustering quality.

Accepted Answer

Since the authors only parallelize the clustering operations inside the partitioner, the speedups the authors obtain on the overall execution time cannot be equal to the number of threads, even in the ideal case.

Accepted Answer

Clustering algorithms are the most time consuming part of the current-state-of-the-art hypergraph partitioning tools that follow the multi-level framework.

Accepted Answer

The array conn[·] of size |V| is necessary to compute the connectivity of the vertex u and all its adjacent vertices in time linearly proportional to the number of adjacent vertices.

Accepted Answer

When the authors integrated the 1/2-approximation algorithm into the coarsening phase of PaToH, the authors observed that better matching quality helps the partitioner to obtain better cutsize.

Accepted Answer

Due to the running time complexity of the maximum quality matching algorithm, it is impractical to obtain the relative performance of the clustering algorithms on their original dataset.

Accepted Answer

The new dataset contains all 289 square matrices in the UFL sparse matrix collection with at least 3, 000 and at most 10, 000 rows.

Accepted Answer

When equipped with the multithreaded clustering algorithms, the cutsize of the partition found by PaToH is almost equal to the original cutsize obtained by using the sequential versions.

Accepted Answer

clustering (HCC) Data: H = (V,N ), maxW , rep for each vertex u ∈ V in a given order doif rep[u] = null then adju ← {} for each net n ∈ nets[u] dofor each vertex v ∈ pins[n] do if v /∈ adju thenadju ← adju ∪ {v}conn[v] ← conn[v] + c[n] v∗ ← u conn∗ ← 0 for each vertex v ∈ adju doif u = v then continuevr ←rep[v] if vr = null thenvr ← v if vr 6= v thenconn[vr] ← conn[vr] + conn[v] conn[v] ← 0 adju ← adju ∪ {vr} \\ {v}1 totW ← w[u] + w[vr] if conn[vr] > conn∗ thenif totW < maxW then conn∗ ← conn[vr] v∗ ← vrfor each vertex v ∈ adju do conn[v] ← 0 if u 6= v∗ then rep[v∗ ] ← v∗ rep[u]← v∗ w[v∗ ] ← w[v∗ ] + w[u](and in their experiments), the authors use the absorption clustering metric (implemented in PaToH) which divides the contribution of each net to the number of its pins.

Accepted Answer

it recomputes the total weight of u and vr (line 3) since new vertices might have been inserted to vr’s cluster by other threads.

Accepted Answer

In 8-thread experiments, the resolution-based algorithm has the highest speedup of 5.87, which is followed by the parallel agglomerative algorithm with a speedup of 5.82.

Accepted Answer

While obtaining matchings having at most 15% worse quality than the optimum, the probabilities are 56% and 28% for the lock- and resolution-based algorithms, respectively.

Accepted Answer

To find the ideal speedups, the authors use Amdahl’s law [28]:speedupideal = 1(1− r) + r#threads (4)where r is the ratio of the total clustering time to the total time of a sequential execution.

Accepted Answer

Another idea is keeping the sequential code (almost) as is, letting the threads create conflicts, and resolving the conflicts later.

Accepted Answer

As muv 6= 0 iff the vertices u and v of H are adjacent, the correspondence implies that a matching among the vertices of H corresponds to a matching on the vertices of G(M).

Accepted Answer

various matching algorithms and heuristics for graphs can be used on G(M) to find a matching among the vertices of H.Bisseling and Manne [21] propose a distributed memory, 1/2-approximate algorithm to find weighted matchings in graphs.

Multithreaded Clustering for Multi-level Hypergraph Partitioning

Chat with Paper

AI Agents for this Paper

Most frequently asked questions

1. What have the authors contributed in "Multithreaded clustering for multi-level hypergraph partitioning" ?

2. What is the way to find the speedups on the overall execution time?

3. What is the time consuming part of the current-state-of-the-art?

4. What is the function of the array conn?

5. What is the way to improve the quality of the partitioner?

6. Why is it impractical to obtain the relative performance of the clustering algorithms on their original?

7. How many square matrices are in the new dataset?

8. What is the cutsize of the partition found by PaToH?

9. what is the metric used for absorption clustering?

10. What is the reason why the thread recomputes the total weight of vr?

11. What is the speedup of the multithreaded algorithms?

12. How is the performance of the algorithm compared to the optimum?

13. How do the authors find the ideal speedups?

14. What is the idea of keeping the sequential code as is?

15. What is the correspondence between the vertices of H and G(M)?

16. How can the authors find a matching among the vertices of G(M)?

Figures

Citations

Rabbit Order: Just-in-Time Parallel Reordering for Fast Graph Analysis

High-Quality Hypergraph Partitioning

More Recent Advances in (Hyper)Graph Partitioning

New Effective Multithreaded Matching Algorithms

Improving graph partitioning for modern graphs and architectures

References

Validity of the single processor approach to achieving large scale computing capabilities

Combinatorial Algorithms for Integrated Circuit Layout

Multilevel hypergraph partitioning: applications in VLSI domain

Recent directions in netlist partitioning: a survey

Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication

Related Papers (5)

The university of Florida sparse matrix collection

Engineering a scalable high quality graph partitioner

A parallel graph partitioning algorithm to speed up the large-scale distributed graph mining

An effective multilevel algorithm for bisecting graphs and hypergraphs

Improving graph partitioning for modern graphs and architectures