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Unformatted text preview: Basic Communication Operations Rajendra V. Boppana UT San Antonio Fall 2011 Review: Modeling Communication Time •Store and forward: distance impacts the overall time significantly t comm = t s + (mt w + t h ) l = t s + mlt w , ignoring t h •Cutthrough: distance does not impact the overall comm. time significantly t comm = t s + lt h + mt w = t s + mt w , ignoring lt h ssumptions •Assumptions –No congestion in the network –Cutthrough routing is assumed –Each node may receive at most one message at a time, and send at most one message at a time –An intermediate node may handle one new cutthrough request at a time; there may be other messages that are already setup for forwarding by the node •A communication step is delivering one or more messages simultaneously. CS 6643 Fall '11 Lec08 2 OnetoAll Broadcast (OAB) •OAB: a process sends some data to all other processes •Reduction: the data from all processes are combined through an associative operator and accumulated at a single destination process CS 6643 Fall '11 Lec08 3 OAB on a Binary Tree •Log(p) communication steps •Each step takes t s + mt w time, ignoring number of hops in a step •Total OAB time = log p (t s + mt w ) •If time for hops are also considered, then total OAB time = log p (t s + mt w ) + (log 2 p + log p) t h CS 6643 Fall '11 Lec08 4 OAB on a Ring or Linear Chain •Emulate the binary tree communication steps •Step i, i= logp, …, 1 , each node that satisfies (id%2 i == 0) sends data to node id+2 i1 •Total OAB time = = log p (t s + mt w ) •Or, log p (t s + mt w ) + (p1) t h •Compute storeandforward communication time! CS 6643 Fall '11 Lec08 5 Reduction on a Ring •Reverse of OAB •Same time complexity CS 6643 Fall '11 Lec08 6 OAB on a 2D Mesh •Phase 1: OAB in row 0, which contains the source node •Phase 2: OAB in each column, with node in row 0 as the source •Total OAB time = 2 [log p 1/2 (t s +mt w ) + (p 1/21) t h ] = log p (t s +mt w ) + 2(p 1/21) t h •Compute OAB time for ddimensional mesh CS 6643 Fall '11 Lec08 7 OAB on a Binary Hypercube •Implement each communication step of the tree algorithm in (t s +mt w + t h ) time •Total OAB time = log p (t s +mt w + t h ) CS 6643 Fall '11 Lec08 8 AlltoAll Broadcast •AAB: each node has data that need to be sent to all other nodes •Alltoall reduction: each node has specific data for other nodes, which need to be combined •Naive approach: AAB is n OABs, alltoall reduction is n singlenode reductions •Better performance with different communication algorithms CS 6643 Fall '11 Lec08 9 AAB on an 8Node Ring CS 6643 Fall '11 Lec08 10 AAB on an 8Node Ring CS 6643 Fall '11 Lec08 11 AAB on a Linear Array and Ring •i= 1, …, p1 steps –node i sends data to (i+1)%p and receives data from (p+i1)%p –In the first step, a node sends its broadcast data –In the following steps, a node sends the newly received data •AAB time? –Each comm. step takes (t s +mt w +t h...
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