Presentation
- 1. A Survey on Topology Mapping for Large Scale Interconnection Networks Soheila Abrishami, Peyman Faizian
- 2. Overview • Background • Definition • Performance metrics • Mapping techniques
- 3. Background • Research in interconnect design can be classified as: • Communication infrastructure (topology) • Communication paradigm (routing, switching) • Evaluation framework (throughput, latency) • Topology/application mapping
- 4. Data Locality • The challenge deals with scalability and can be expressed in several ways: • How to use the maximum of the available resources at their full potential? • How to do so with an energy consumption that remains acceptable? • One global and practical answer to these questions is to improve the “Data Locality” of parallel applications
- 5. Data Locality… • Data locality: the way the data are placed, accessed and moved by the multiple hardware processing units of the underlying target architecture • Improving data locality can cause: • Reduced Communication cost • Decrease in application’s execution time • Decrease in energy consumption
- 6. Mapping • One way to improve data locality is to dedicate physical processing units to their specific software processing entities • This means that matching between the application virtual topology and the target hardware architecture has to be determined
- 7. Mapping… • Virtual topology: Expresses the existing dependencies between software processing entities • Static: number of processing entities and the dependencies between these entities do not change • Dynamic: when one of the two above conditions (possibly both) is not fulfilled. • In addition, the maximum of details regarding the target hardware have to be gathered.
- 8. Mapping… • The matching between the virtual and the physical topologies is achievable in both ways • the virtual topology can be mapped on to the physical one • the physical topology can also be mapped onto the virtual one
- 9. Topology mapping • The network is typically modeled by a weighted graph 𝐻 = 𝑉𝐻, 𝑊𝐻, 𝑅 𝐻 • 𝑉𝐻: represent the execution units • 𝑊𝐻(𝑢, 𝑣): represent the weight of the edges between two vertices 𝑢 and 𝑣 • 𝑅 𝐻: represent the routing as a probability distribution • The static application graph is often modeled as a weighted graph 𝐴 = 𝑉𝐴, 𝑤 𝐴 • 𝑉𝐴: represents the set of communicating processes • 𝑤 𝐴 𝑢, 𝑣 : represents some metric for the communication between two processes 𝑢, 𝑣
- 10. Topology mapping… • The topology mapping considers mappings 𝜎 ∶ 𝑉𝐴 → 𝑉𝐻 • Each concrete mapping 𝜎 has two metrics: • Dilation: is defined as either the maximum or the sum of the pairwise distances of neighbors in 𝐴 mapped to 𝐻. (correlate with the dynamic energy consumption of the network) • Congestion: counts how many communication pairs use a certain link. (correlates strongly with the execution time of bulk-synchronous parallel applications)
- 11. Mapping Techniques Finding a perfect mapping (wrt to a specific metric) is NP-Complete. • LP based algorithms • Constructive approaches (greedy) • Partitioning approaches • Transformative approaches • Graph similarity based approaches
- 12. LP formulation • Given a topology G (links and bandwidths) • Given a virtual topology H (communications graph) • Find a mapping from H -> G such that: • Maximum throughput • Minimum latency • Minimum congestion • Minimum dilation • Software solutions are available to solve the linear program
- 13. Greedy Approaches • Select two starting vertices u, v from G and H respectively • Local • Add next vertices from the neighborhood of initial vertices • Global • Add next vertices based on a global property (i.e., node degrees) • Continue until finding a full mapping • The end result relies heavily on the choice of first vertices • Compute mappings based on different initial choices and select the best one • Define some kind of primary conditions to choose the initial vertices
- 14. Partitioning Approaches • Based on k-way graph partitioning (i.e., 2-way partitioning) • H and G graphs are recursively cut into k parts based on a property (i.e., minimum weighted edge-cut) • The resulting graphs are mapped together using the same approach • Several heuristics are available to perform the partitioning task which is NP-Complete
- 15. Transformative approaches • Start with an initial mapping • Iteratively transform it to better ones • Typically evolutionary techniques are used • Genetic Algorithms • Ant Colony Optimization • … • Fitness measure • Delay • Power consumption • …
- 16. Graph Similarity Based Approaches • Graph adjacency matrix can be modeled as a sparse matrix • Mapping problem would be transformed to bringing two matrices into a similar shape • One possible approach: • Reduce the bandwidth of two sparse matrices • Transform them to diagonal matrices • Do the mapping
- 17. Graph Similarity Based Approaches
- 18. Final Comments • None of the techniques give optimal results in all cases • Topology specific mapping approaches seem to work better • Some papers propose using a combination of above approaches to achieve better results • Data locality is not always desirable (i.e., dragonfly) • So far a few papers have explored parallelized mapping techniques • Better outcomes if we consider the routing algorithms while mapping