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**U of Houston – Clear Lake**

Adaptive Latency-Aware Parallel Resource Mapping: Task Graph Scheduling Heterogeneous Network Topology Liwen Shih, Ph.D. Computer Engineering U of Houston – Clear Lake

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**ADAPTIVE PARALLEL TASK TO NETWORK TOPOLOGY MAPPING**

Latency-adaptive: Topology Traffic Bandwidth Workload System hierarchy Thread partition: Coarse Medium Fine

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**Fine-Grained Mapping System [Shih 1988]**

Parallel Mapping Compiler- vs. run- time Task migration Vertical vs. Horizontal Domain decomposition Data vs. Function Execution order Eager data-driven vs. Lazy demand-driven

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**PRIORITIZE TASK DFG NODES**

Task priority factors: Level depth Critical Paths In/Out degree Data flow partial order: {(n7n5), (n7n4), (n6n4), (n6n3), (n5n1), (n4n2), (n3n2), (n2n1)} total task priority order: {n1 > n2 > n4 > n3 > n5 > n6 > n7} P2 thread: {n1>n2>n4>n3>n6} P3 thread: {n5 > n7}

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**SHORTEST-PATH NETWORK ROUTING**

Shortest latency and routes are updated after each task-processor allocation.

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**Adaptive A* Parallel Processor Scheduler**

Given a directed, acyclic task DFG G(V, E) with task vertex set V connected by data-flow edge set E, And a processor network topology N(P , C) with processor node set P connected by channel link set C Find a processor assignment and schedule S: V(G) P (N) S minimizes total parallel computation time of G. A* Heuristic mapping reduces scheduling complexity from NP to P

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**Demand-Driven Task-Topology mapping**

STEP 1 – assign a level to each task node vertex in G. STEP 2 – count critical paths passing through each DFG edge and node with a 2-pass bottom-up and then up-down graph traversal. STEP 3 – initially load and prioritize all deepest level task nodes that produce outputs, to the working task node list. STEP 4 – WHILE working task node list is not empty, schedule a best processor to the top priority task, and replace it with its parent task nodes inserted onto the working task node priority list.

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**Demand-Driven Processor Scheduling**

STEP 4 – WHILE working task node list is not empty: BEGIN STEP 4.1 – initialize if first time, otherwise update inter-processor shortest-path latency/routing table pair affected by last task-processor allocation. STEP 4.2 – assign a nearby capable processor to minimize thread computation time for the highest priority task node at the top of the remaining prioritized working list. STEP 4.3 – remove the newly scheduled task node, and replace it with its parent nodes, which are to be inserted/appended onto the working list (demand-driven) per priority, based on tie-breaker rules, which along with node level depth, estimate the time cost of the entire computation tread involved. END{WHILE}

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**QUANTIFY SW/HW MAPPING QUALITY**

Example 1 – Latency-Adaptive Tree-Task to Tree-Machine Mapping Example 2 – Scaling to Larger Tree-to-Tree Mapping Example 3 – Select the Best Processor Topology Match for an Irregular Task Graph

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**Example 1 – Latency-Adaptive Tree-Task to Tree-Machine Mapping**

K-th Largest Selection Will tree Algorithm [3] match tree machine [4]?

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**Example 1 – Latency-Adaptive Tree-Task to Tree-Machine Mapping**

Adaptive mapping moves toward sequential processing when inter/intra communication latency ratio increase.

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**Example 1 – Latency-Adaptive Tree-Task to Tree-Machine Mapping**

Adaptive Mapper allocates fewer processors and channels with fewer hops.

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**Example 1 – Latency-Adaptive Tree-Task to Tree-Machine Mapping**

Adaptive Mapper achieves higher speedups consistently. (Bonus! pipeline processing speedup and be extrapolated when inter/intra communication latency ratio <1)

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**Example 1 – Latency-Adaptive Tree-Task to Tree-Machine Mapping**

Adaptive Mapper results in better efficiencies consistently. (Bonus! % pipeline processing efficiency can be extrapolated when inter/intra communication latency ratio <1)

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**Example 2 – Scaling to Larger Tree-to-Tree Mapping**

Adaptive Mapper achieves sub-optimal speedups as tree sizes scaled larger speedups, still trailing fixed tree-to-tree mapping closely.

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**Example 2 – Scaling to Larger Tree-to-Tree Mapping**

Adaptive Mapper is always more cost-efficient using less resource, with compatible sub-optimal speedups to fixed tree-to-tree mapping as tree sizes scaled.

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**Example 3 – Select the Best Processor Topology Match for an Irregular Task Graph**

Lack of matching topology clues for irregular shaped Robot Elbow Manipulator [5] 105 task nodes, 161 data flow edges 29 node levels

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**Example 3 – Select the Best Processor Topology Match for an Irregular Task Graph**

Candidate topologies Compare schedules for each topology Farther processors may not be selected Linear Array Tree

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**Example 3 – Select the Best Processor Topology Match for an Irregular Task Graph**

Best network topology performers (# channels) Complete (28) Mesh (12) Chordal ring (16) Systolic array (16) Cube (12)

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**Example 3 – Select the Best Processor Topology Match for an Irregular Task Graph**

Fewer processors selected for higher diameter networks Tree Linear Array

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**Example 3 – Select the Best Processor Topology Match for an Irregular Task Graph**

Deducing network switch hops Low multi-hop data exchanges < 10% Moderate 0-hop of 30% to 50% High near-neighbor direct 1-hop 50% to 70%

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**Future Speed/Memory/Power Optimization**

Latency-adaptive Topology Traffic Bandwidth Workload System hierarchy Thread partition Coarse Mid Fine Latency/Routing tables Neighborhood Network hierarchy Worm-hole Dynamic mobile network routing Bandwidth Heterogeneous system Algorithm-specific network topology

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References

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**Professor in Computer Engineering University of Houston – Clear Lake**

Q & A? Liwen Shih, Ph.D. Professor in Computer Engineering University of Houston – Clear Lake

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xScale13 paper

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Thank You!

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