Load Balancing How? –Partition the computation into units of work (tasks or jobs) –Assign tasks to different processors Load Balancing Categories –Static (load assigned before application runs) –Dynamic (load assigned as applications run) oCentralized (Tasks assigned by the master or root process) oDe-centralized (Tasks reassigned among slaves) –Semi-dynamic (application periodically suspended and load balanced) Load Balancing Algorithms are: –Adaptive if they adapt to different system load levels oThresholds control how they adapt –Stable if load balancing traffic is independent of load levels –Symmetric if both senders and receivers initiate action –Effective if load balancing overhead is minimal A load is balanced if no processes are idle

Improving the Load Balance By realigning processing work, we improve speed-up

Static Load Balancing Round Robin –Tasks given to processes in sequential order. –If there are more tasks than processors, the allocation wraps around to the first Randomized –Tasks are assigned randomly to processors Partitioning – Tasks represented by a graph –Recursive Bisection –Simulated Annealing –Genetic Algorithms –Multi-level Contraction and Refinement Advantage –Simple to implement –Minimal run time overhead Disadvantages –Predicting execution times is often not knowable before execution –Affect of communication dynamics is often not considered –The number of iterations is often indeterminate Done prior to executing the parallel application

Dynamic Load Balancing Centralized –A single process hands out tasks –Processes ask for more work when their processing completes –Double buffering can be effective Decentralized –Processes detect that their work load is low –Processes can sense an overload condition This occurs when new tasks are spawned during execution –Questions Which neighbors are part of the rebalancing? How should thresholds be set? What are the communications needed to balance? How often should balancing occur? Done as a parallel application executes

Centralized Load Balancing Master Processor While ( task=Remove()) != null) Receive(p i, request_msg) Send(p i, task) While(more processes) Receive(p i, request_msg) Send(p i, termination_msg) Slave Processor task = Receive(p master, message) While (task!=terminate) Process task Send(p master, request_msg) task = Receive(p master, message) Work Pool, Processer Farm, or Replicated Worker Algorithm Slaves Master In this case, the slaves don’t spawn new tasks

Centralized Termination Necessary Requirements –The task queue is empty –Every process has requested another task Master Processor WHILE (true) Receive(p i, msg) IF msg contains a new task Add the new task to the task queue ELSE Add p i to wait queue and waitCount++ IF waitCount>0 and task queue not empty Remove p i & task respectively from wait & task queue Send(task, p i ) and waitCount—- IF waitCount==P THEN send termination messages & exit How do we terminate when slave processes spawn new tasks?

Decentralized Load Balancing There is no Master Processor Each Processor maintains a work queue Processors interact with neighbors to request and distribute tasks (Worker processes interact among themselves)

Decentralized Mechanisms Receiver Initiated –Process requests tasks when it is about to go idle –Effective when the load is heavy –Unstable when the load is light (A request frequency threshold is necessary) Sender Initiated –Process with a heavy load distributes the excess –Effective when the load is heavy –Can cause thrashing when loads are heavy (synchronizing system load with neighbors is necessary) Balancing is among a subset of the total running processes Application Balancing Algorithm Task Queue

Process Selection Global or Local? –Global involves all of the processors of the network May require expensive global synchronization May be difficult if the load dynamic is rapidly changing –Local involves only neighbor processes Overall load may not be balanced Easier to manage and less overhead than the global approach Neighbor selection algorithms –Random: randomly choose another process Easy to implement and studies show reasonable results –Round Robin: Select among neighbors using modular arithmetic Easy to implement. Results similar to random selection –Adaptive Contracting: Issue bids to neighbors; best bid wins Handshake between neighbors needed Possible to synchronize loads

Choosing Thresholds How do we estimate system load? –Synchronization averages task queue length or processes –Average number of tasks or projected execution time When is the load low? –When a process is about to go idle –Goal: prevent idleness, not achieve perfect balance –A low threshold constant is sufficient When is the load high? –When some processes have many tasks and others are idle –Goal: prevent thrashing –Synchronization among processors is necessary –An exponentially growing threshold works well What is the job request frequency? –Goal: minimize load balancing overhead

Gradient Algorithm Node Data Structures –For each neighbor Distance, in hops, to the nearest lightly-loaded process –A load status flag indicating if the current processor is lightly- loaded, or normal Routing –Spawned jobs go to the nearest lightly-loaded process Local Synchronization –Node status changes are multicast to its neighbors L Maintains a global pressure grid

Symmetric Broadcast Networks (SBN) Characteristics –A unique SBN starts at each node –Each SBN is lg P deep –Simple operations algebraically compute successors –Easily adapts to the hypercube Algorithm –Starts with a lightly loaded process –Phase 1: SBN Broadcast –Phase 2: Gather task queue lengths –Load is balanced during the load and gather phases Global Synchronization Stage 0 Stage 1 Stage 2 5 Stage 3 Successor 1 = (p+2 s-1 ) %P; 1≤s ≤ 3 Successor 2 = (p-2 s-1 ); 1≤s<3 Note: If successor 2<0 successor2 +=P

Line Balancing Algorithm Master processor adds to the pipeline Slave processors –Request and receives tasks if queue not full –Pass tasks on if task request is posted Non blocking receives are necessary to implement this algorithm Uses a pipeline approach Request task if queue not full Receive task from request Deliver task to p i+1 p i+1 requests task Dequeue and process task pipi Note: This algorithm easily extends to a tree topology

Semi-dynamic Pseudo code Run algorithm Time to check balance? Suspend application IF load is balanced, resume application Re-partition the load Distribute data structures among processors Resume execution Partitioning –Model application execution by a partitioning graph –Partitioning is an NP-Complete problem –Goals: Balance processing and minimize communication –Partitioning Heuristics Recursive Bisection, Simulated Annealing, Multi-level, MinEx –Data Redistribution Goal: Minimize the data movement cost

Partitioning Graph P2 R1 P5 R3 P8 R3 P4 R1 P6 R6 P2 R1 P9 R6 P4 R4 P7 R5 P1 P2 c4 c6 c2 c1 c7 c1 c3 c8 c5 c3 P1 Load = ( ) + ( ) = 37 P2 Load = ( ) + ( ) = 40 Question: When can we move a task to improve load balance?

Distributed Termination Insufficient condition for distributed termination –Empty task queues at every process Sufficient condition for distributed termination requires –All local termination conditions satisfied –No messages in transit that could restart an inactive process Termination algorithms –Acknowledgment –Ring –Tree –Fixed energy distribution

Acknowledgement Termination Process Receives task –Immediately acknowledge if source is not parent –Acknowledge parent as process goes idle Process goes idle after it –completes processing local tasks –Sends all acknowledgments –Receives all acknowledgments Note –A process always becomes inactive before its parent –The application can terminate when the master goes idle Active Inactive First task Acknowledge first task PiPi PjPj Definition : Parent is the process sending initial task to a process

Single Pass Ring Termination Pseudo code P 0 sends a token to P 1 when it goes idle P i receives token IF P i is idle it passes token to P i+1 ELSE P i sends token to P i+1 when it goes idle P 0 receives token Broadcast final termination message Assumptions –Processes cannot reactivate after going idle –Processes cannot pass new tasks to an idle process P0P0 P1P1 P2P2 PnPn Token

Dual Pass Ring Termination Pseudo code WHEN P 0 goes idle, it sends a white token to p 1 WHEN P i sends a task to P j where j<i P i becomes a black process WHEN P i>0 receives token and goes idle IF P i is a black process P i colors the token black, P i becomes White ELSE P i sends token to P (i+1)%n unchanged in color IF P 0 receives token and is idle IF token is White, application terminates ELSE p o sends a White token to P 1 Handles task sent to a process that already passed the token on Key Point: Token and processors are colored either White or Black

Tree Termination When a Leaf process terminates, it sends a token to it’s parent process Internal nodes send tokens to it’s parent when all of its children processes terminate When the root node receives the token, the application can terminate Either one-pass or two pass algorithms can apply AND Leaf Nodes Terminated

Fixed Energy Termination P 0 starts with full energy –When P i receives a task, it also receives an energy allocation –When P i spawns tasks, it assigns them to processors with additional energy allocations within its allocation –When a process completes it returns its energy allotment The application terminates when the master becomes idle Implementation –Problem: Integer division eventually becomes zero –Solution: oUse two level energy allocation oThe generation increases each time energy value goes to zero Energy defined by an integer or long value

Example: Shortest Path Problem Definitions Graph: Collection of nodes (vertices) and edges Directed Graph: Edge can be traversed in only one direction Weighted Graph: Edges have weights that define cost Shortest Path Problem: Find the path from one node to another in a weighted graph that has the smallest accumulated weights Applications 1.Shortest distance between points on a map 2.Quickest travel route 3.Least expensive flight path 4.Network routing 5.Efficient manufacturing design

Climbing a Mountain Weights: expended effort Directed graph –Effort in one direction ≠ effort in another direction –Ex: Downhill versus uphill ABCDEF A10 B C14 D9 E17 F A BC D E F Adjacency Matrix C8 D14X E9X F17X X B10X D13 E24 F51 A B C D E F Adjacency List Graphic Representation

Moore’s Algorithm Assume –w[i][j] =weight of edge (i,j) –Dist[v] = distance to vertex v –Pred[v] = predecessor to vertex v Pseudo code Insert the source vertex into a queue For each vertex, v, dist[v]=∞ infinity, dist[0] = 0 WHILE (v = dequeue() exists) FOR (j=; j<n; j++) newdist = dist[i] + w[i][j] IF (newdist < dist[j]) dist[j] = newdist pred[j] = I append(j) Less efficient than Dijkstra but more easily parallelized ij didi w i,j djdj d j =min(d j,d i +w i,j )

Graph Analysis Stages A 0∞∞∞∞∞ B 010∞∞∞∞ E FEDC DC CE ABCDEF Vertex QueueDist[j] EDC

Centralized Work Pool Solution The Master maintains –The work pool queue of unchecked vertices –The distance array Every slave holds –The graph weights which is static The Slaves –Request a vertex –Compute new minimums –Send updated distance values and vertex to master The Master –Appends received vertices to its work queue –Sends new vertex and the updated distance array.

Distributed Work Pool Solution Data held in each processor –The graph weights –The distances to vertices stored locally –The processor assignments When a process receiving a distance: –If its local value is reduced oUpdates its local value of dist[v] oSend distances to adjacent vertices to appropriate processors Notes –Inefficient with one vertex per processor oPoor computation to communication ratio oMany processors can be inactive –One of the termination algorithms is necessary