Electrical Engineering Department Technion, Haifa, Israel Routing Table Minimization for Irregular Mesh No. Cs Evgeny Bolotin, Israel Cidon, Ran Ginosar, Avinoam Kolodny QNo. C Research Group Technion 1 Evgeny Bolotin – Efficient Routing, DATE 2007
Motivation Generic No. C: • Mesh Topology § Low Cost Links • Shortest Path (SP) Static Function Routing § § § Low Cost Router Power-Efficient Communication Low Cost Interfaces (no reordering) Practical System Example: XY routing Practical No. C (QNo. C and others) ü Custom/Irregular ü Low Cost 2 Evgeny Bolotin – Efficient Routing, DATE 2007
Routing in Irregular Mesh No. C The Problem: Simple Function (e. g. XY) is not working ü Around the Block ü Dead End 3 Evgeny Bolotin – Efficient Routing, DATE 2007
Traditional Approach Traditional Irregular Routing • Distributed Routing – Tables in Routers § § Output Port for All Destinations Size of Tables ~ • Source Routing – Tables in Sources § § List of routing tags (for each hop) for All Destinations Size of Tables ~ Ø Large Area/Power Cost Ø Increased Access Time Can we do better than full routing tables? 4 Evgeny Bolotin – Efficient Routing, DATE 2007
Low Cost Routing Solution: 1. Don’t Use Full Routing Tables (Customize) § Store only relevant destinations Routing Table Cost : Area [gates] ≈ Sizof(Entries) + Sizof (Lookup Logic) Power ≈ Const * Area 2. Minimize Routing Table Size: Routing Function + Reduced Routing Table ( for deviations only) 5 Evgeny Bolotin – Efficient Routing, DATE 2007
Minimize Table Entries • Distributed Routing: § § Default Function (“Go XY” or “Don’t turn”) Reduced Routing Tables (for deviations) Ø “Go XY” – XY Deviations Table (XYDT) Routing Entry Ø “Don’t Turn” – Turn-Table (TT) No Entries 6 Evgeny Bolotin – Efficient Routing, DATE 2007 Routing Entry No Entries
Minimize Table Entries • Source Routing: § § Default Function (“Go XY” or “Don’t turn”) Reduced routing-tag list (only for deviations) Ø Source Routing for Deviation Points (SRDP) Example: • Specific routers are Deviation Points • Default function routing in other routers 7 Evgeny Bolotin – Efficient Routing, DATE 2007
Path Selection Algorithms Shortest Path with Minimal Number of Turns: Build Auxiliary Graph: Turns-Graph ‘K’- Large Number, price of “Hop” ‘ 1’- Price of “Turn” ‘ 0’- Price of “Don’t Turn” Original Apply Shortest Path (Dijkstra) on Turns-Graph: • Primary objective: minimal number of hops • Secondary objective: minimal number of turns 8 Evgeny Bolotin – Efficient Routing, DATE 2007 Turns-Graph
Path Selection Algorithms Turn-Table (TT) Algorithm Among all shortest paths between all S-D pairs, choose covering set of paths that minimize the total number of entries in the network Turns-Tables. Question: Is it Shortest Path with Minimal Number of Turns? Answer: No! Example: Choose: • Scenario A: Green path makes 3 Turns • Scenario B: Green path makes 2 Turns A: Green doesn’t add new entries (uses existing) Scenario A TT Idea: Combine routing paths from different sources 9 Evgeny Bolotin – Efficient Routing, DATE 2007 Scenario B
Turn-Table (TT) Algorithm TT Algorithm (greedy) – Informal Explanation: Iteration #1 Calc Distances Choose Closest Src Create Path to D Iteration #2 Update Distances Choose Closest Src Create Path to D In each iteration choose a shortest path from closest Src to D, or to an already existing path to D, which adds the minimal number of turns 10 Evgeny Bolotin – Efficient Routing, DATE 2007
XY-Deviation Table (XYDT) XYDT Problem definition: Among all shortest paths between each S-D pair, select a path that minimizes number of routing steps which deviate from XY routing policy. XYDT Algorithm Outline: For each destination D: • Sort nodes according to distance from D • For nodes at same distance from D: § Among all shortest-path steps choose XY step if exists • Repeat until paths from all sources are found 11 Evgeny Bolotin – Efficient Routing, DATE 2007
Further Minimization Tricks • Turn-Table Routing: § At source router every step is turn § Default Direction at the source router • XY-Deviation Table Routing: § Save entry if XY-port is missing and routing goes YX No Entries 12 Evgeny Bolotin – Efficient Routing, DATE 2007 Routing Entry
Source Routing for Deviation Points (SRDP) The Idea: Specific routers are Deviation Points Default function for all other routers SRDP Algorithm Outline: • Find paths using algorithms above • Find deviation points (DPs) • Calculate Reduced SRDP headers 13 Evgeny Bolotin – Efficient Routing, DATE 2007
Evaluation Method • Efficient Routing Path Selection Algorithms § Distributed/Source Routing § “XY”/ “ Don’t Turn” • Irregular grid § Random holes insertion • Inter-module Connections Matrix • 14 § Random hotspots insertion o Connection to hotspot (high probability) o Connection to non-hotspot (low probability) § Real examples - Video Processing Apps (MPEG, VOPD) Compare Cost [gate count] § Tables containing relevant destination only § Our method : Routing function + Table for deviations Evgeny Bolotin – Efficient Routing, DATE 2007
Results - Typical No. C Savings in small system with high irregularity and few destinations Distributed Routing “Turns Table” 3 X “XY Deviations Table” Source Routing 15 8 X “SR Deviation Points” 2. 5 X Evgeny Bolotin – Efficient Routing, DATE 2007
Results - Typical No. C Savings in large system with low irregularity and many destinations Distributed Routing “Turns Table” 3. 7 X “XY Deviations Table” Source Routing 16 34 X “SR Deviation Points” 2 X Evgeny Bolotin – Efficient Routing, DATE 2007
Results –Video Apps Savings in video processing app. system Distributed Routing “Turns Table” 4. 4 X “XY Deviations Table” Source Routing 17 40 X “SR Deviation Points” 2. 9 X Evgeny Bolotin – Efficient Routing, DATE 2007
Savings Scaling of Savings : DR and SR Network Size 18 Evgeny Bolotin – Efficient Routing, DATE 2007
Scaling: Source vs. Distributed Routing Large system with low irregularity and many destinations • Good Scaling with Distributed Routing • Best Scaling with XYDT 19 Evgeny Bolotin – Efficient Routing, DATE 2007
Summary • The Problem – Low Cost Routing In Irregular Mesh • Idea: Combine Default Function + Reduced Deviation Tables §Distributed Routing and Source Routing • Path Selection Algorithms §Shortest path + Minimum Total Table Entries • Numerical Results §Significant Cost Reduction – DR(40 X); SR(3 X) §Scalability of Savings §Good Scalability of Distributed Routing (XYDT the best) 20 Evgeny Bolotin – Efficient Routing, DATE 2007
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