Penn ESE535 Spring2015 -- DeHon 1 ESE535: Electronic Design Automation Day 2: January 26, 2015...
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Transcript of Penn ESE535 Spring2015 -- DeHon 1 ESE535: Electronic Design Automation Day 2: January 26, 2015...
![Page 1: Penn ESE535 Spring2015 -- DeHon 1 ESE535: Electronic Design Automation Day 2: January 26, 2015 Covering Work preclass exercise.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649eb55503460f94bbdff7/html5/thumbnails/1.jpg)
Penn ESE535 Spring2015 -- DeHon 1
ESE535:Electronic Design Automation
Day 2: January 26, 2015
Covering
Work preclass exercise
![Page 2: Penn ESE535 Spring2015 -- DeHon 1 ESE535: Electronic Design Automation Day 2: January 26, 2015 Covering Work preclass exercise.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649eb55503460f94bbdff7/html5/thumbnails/2.jpg)
Feedback -- Piazza
• Last lecture– Average Pace 4 – everyone agreed was fast
• Posted followup on Piazza• Identified a correction on assignment 2
on Piazza
….only 10 people signed up on Piazza
Penn ESE535 Spring2015 -- DeHon 2
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Penn ESE535 Spring2015 -- DeHon 3
Today: Covering Problem
• Implement a “gate-level” netlist in terms of some library of primitives
• General Formulation– Make it easy to change technology– Make it easy to experiment with library
requirements • Evaluate benefits of new cells…• Evaluate architecture with different primitives
Behavioral (C, MATLAB, …)
RTL
Gate Netlist
Layout
Masks
Arch. SelectSchedule
FSM assign
Two-level, Multilevel opt.CoveringRetiming
PlacementRouting
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Penn ESE535 Spring2015 -- DeHon 4
Input
1. netlist (logical circuit)
2. library
• represent both in normal form:– nand gate– inverters
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Penn ESE535 Spring2015 -- DeHon 5
Elements of a library - 1
INVERTER 2
NAND2 3
NAND3 4
NAND4 5
Element/Area Cost Tree Representation (normal form)
Example: Keutzer
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Penn ESE535 Spring2015 -- DeHon 6
Elements of a library - 2
AOI21 4
AOI22 5
Element/Area Cost Tree Representation (normal form)
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Penn ESE535 Spring2015 -- DeHon 7
Input Circuit Netlist
``subject DAG’’
• Each wire is a network (net).• Each net has a single source (the gate that drives it).• In general, net may have multiple sinks (gates that take as input)
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Penn ESE535 Spring2015 -- DeHon 8
Input Circuit Netlist
``subject DAG’’
• A list of the nets (netlist) fully describes the circuit0 nand 1 61 inv 22 nand 3 4
0
1
6
23
4
5
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Penn ESE535 Spring2015 -- DeHon 9
Problem Statement
into this library
Find an ``optimal’’ (in area, delay, power) mapping of this circuit (DAG)
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Penn ESE535 Spring2015 -- DeHon 10
Why covering now?
• Nice/simple cost model• Problem can be solved well
– somewhat clever solution
• General/powerful technique• Show off special cases
– harder/easier cases
• Show off things that make hard• Show off bounding
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Penn ESE535 Spring2015 -- DeHon 11
What’s the Problem? Trivial Covering
subject DAG
7 NAND2 (3) = 215 INV (2) = 10
Area cost 31
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Penn ESE535 Spring2015 -- DeHon 12
Preclass 1
• Direct covering cost?
2 3 4 6
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Penn ESE535 Spring2015 -- DeHon 13
Preclass 3 & 4
• Least Area Cover? (associated area?)– How did you get?
2 3 4 6
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Penn ESE535 Spring2015 -- DeHon 14
Cost Models
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Penn ESE535 Spring2015 -- DeHon 15
Cost Model: Area
• Assume: Area in gates• or, at least, can pick an area/gate
– so proportional to gates• e.g.
– Standard Cell design– Standard Cell/route over cell– Gate array
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16
Standard Cells• Lay out gates so that heights match
– Rows of adjacent cells– Standardized sizes
• Motivation: ease place and route
Penn ESE535 Spring2015 -- DeHon 16
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Penn ESE535 Spring2015 -- DeHon
Standard Cell Area
inv nand3
All cellsuniformheight
Width ofchanneldeterminedby routing
Cell area
17
Width of channelfairly constant?
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Penn ESE535 Spring2015 -- DeHon 18
Cost Model: Delay
• Delay in gates– at least assignable to gates
• Twire << Tgate
• Twire ~=constant
– delay exclusively/predominantly in gates• Gates have Cout, Cin
• lump capacitance for output drive• delay ~ Tgate + fanoutCin
• Cwire << Cin
• or Cwire can lump with Cout/Tgate
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Penn ESE535 Spring2015 -- DeHon 23
Cost Models• Why do I show you models?
– not clear there’s one “right” model– changes over time– you’re going to encounter many different kinds of
problems– want you to see formulations so can critique and
develop own– simple cost models make problems tractable
• are surprisingly adequate– simple, at least, help bound solutions– may be wrong today…need to rethink
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Penn ESE535 Spring2015 -- DeHon 24
Approaches
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Penn ESE535 Spring2015 -- DeHon 25
Greedy work?
• Greedy = pick next locally “best” choice
2 3 4 6
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Penn ESE535 Spring2015 -- DeHon 26
Greedy InOut
6
4
2
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Penn ESE535 Spring2015 -- DeHon 27
Greedy InOut
8
11
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Penn ESE535 Spring2015 -- DeHon 28
Greedy OutIn
6
4
2
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Penn ESE535 Spring2015 -- DeHon 29
Greedy OutIn
8
11
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Penn ESE535 Spring2015 -- DeHon 30
But…
4 2 4 = 10
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Penn ESE535 Spring2015 -- DeHon 31
Greedy Problem
• What happens in the future (elsewhere in circuit) will determine what should be done at this point in the circuit.
• Can’t just pick best thing for now and be done.
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Penn ESE535 Spring2015 -- DeHon 32
Brute force?
• Pick a node (output)• Consider
– all possible gates which may cover that node
– branch on all inputs after cover– pick least cost node
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Penn ESE535 Spring2015 -- DeHon 33
Pick a Node
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Penn ESE535 Spring2015 -- DeHon 34
Brute force?
• Pick a node (output)• Consider
– all possible gates which may cover that node– recurse on all inputs after cover– pick least cost node
• Explore all possible covers– can find optimum
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Penn ESE535 Spring2015 -- DeHon 35
Analyze brute force?
• Time?
• Say P patterns, constant time to match each– (if patterns long could be > O(1))
• P-way branch at each node…• How big is tree?
• …exponential O((P)depth)
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Penn ESE535 Spring2015 -- DeHon 36
Structure inherent in problem to exploit?
• What structure exists?
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Penn ESE535 Spring2015 -- DeHon 37
Structure inherent in problem to exploit?
• There are only N unique nodes to cover!
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Penn ESE535 Spring2015 -- DeHon 38
Structure
• If subtree solutions do not depend on what happens outside of its subtree– separate tree– farther up tree
• Should only have to look at N nodes.• Time(N) = N*P*T(match)
– w/ P fixed/bounded linear in N– w/ cleverness work isn’t P*T(match) at every node
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Penn ESE535 Spring2015 -- DeHon 39
Idea Re-iterated
• Work from inputs• Optimal solution to subproblem is
contained in optimal, global solution• Find optimal cover for each node• Optimal cover:
– examine all gates at this node– look at cost of gate and its inputs– pick least
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Penn ESE535 Spring2015 -- DeHon 40
Work front-to-back
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Penn ESE535 Spring2015 -- DeHon 41
Work Example (area)
library
2 3 4 5 4 5
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Penn ESE535 Spring2015 -- DeHon 42
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
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Penn ESE535 Spring2015 -- DeHon 43
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
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Penn ESE535 Spring2015 -- DeHon 44
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
Consider all patterns
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Penn ESE535 Spring2015 -- DeHon 45
Elements of a library - 1
INVERTER 2
NAND2 3
NAND3 4
NAND4 5
Element/Area Cost Tree Representation (normal form)
Example: Keutzer
Copy to board
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Penn ESE535 Spring2015 -- DeHon 46
Elements of a library - 2
AOI21 4
AOI22 5
Element/Area Cost Tree Representation (normal form)
![Page 43: Penn ESE535 Spring2015 -- DeHon 1 ESE535: Electronic Design Automation Day 2: January 26, 2015 Covering Work preclass exercise.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649eb55503460f94bbdff7/html5/thumbnails/43.jpg)
Penn ESE535 Spring2015 -- DeHon 47
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
Consider all patterns
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Penn ESE535 Spring2015 -- DeHon 48
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
3+3+2=8
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Penn ESE535 Spring2015 -- DeHon 49
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
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Penn ESE535 Spring2015 -- DeHon 50
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
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Penn ESE535 Spring2015 -- DeHon 51
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
3+2=5
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Penn ESE535 Spring2015 -- DeHon 52
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5
![Page 49: Penn ESE535 Spring2015 -- DeHon 1 ESE535: Electronic Design Automation Day 2: January 26, 2015 Covering Work preclass exercise.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649eb55503460f94bbdff7/html5/thumbnails/49.jpg)
Penn ESE535 Spring2015 -- DeHon 53
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5
ConsiderAll patterns
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Penn ESE535 Spring2015 -- DeHon 54
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
53+5=8
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Penn ESE535 Spring2015 -- DeHon 55
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
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Penn ESE535 Spring2015 -- DeHon 56
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
![Page 53: Penn ESE535 Spring2015 -- DeHon 1 ESE535: Electronic Design Automation Day 2: January 26, 2015 Covering Work preclass exercise.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649eb55503460f94bbdff7/html5/thumbnails/53.jpg)
Penn ESE535 Spring2015 -- DeHon 57
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
8+2+3=13
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Penn ESE535 Spring2015 -- DeHon 58
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13
![Page 55: Penn ESE535 Spring2015 -- DeHon 1 ESE535: Electronic Design Automation Day 2: January 26, 2015 Covering Work preclass exercise.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649eb55503460f94bbdff7/html5/thumbnails/55.jpg)
Penn ESE535 Spring2015 -- DeHon 59
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
1313+2=15
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Penn ESE535 Spring2015 -- DeHon 60
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
133+2+4=9
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Penn ESE535 Spring2015 -- DeHon 61
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13 9
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Penn ESE535 Spring2015 -- DeHon 62
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13 99+4+3=16
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Penn ESE535 Spring2015 -- DeHon 63
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13 98+2+4+4=18
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Penn ESE535 Spring2015 -- DeHon 64
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13 9 16
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Penn ESE535 Spring2015 -- DeHon 65
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13 9 1616+2=18
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Penn ESE535 Spring2015 -- DeHon 66
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13 9 16 13+5+4=22
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Penn ESE535 Spring2015 -- DeHon 67
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13 9 16 18
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Penn ESE535 Spring2015 -- DeHon 68
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13 9 16 1818+3=21
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Penn ESE535 Spring2015 -- DeHon 69
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13 9 16 189+4+4=17
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Penn ESE535 Spring2015 -- DeHon 70
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13 9 16 188+2+4+5=19
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Penn ESE535 Spring2015 -- DeHon 71
Work Example (area)
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13 9 16 18 17
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Penn ESE535 Spring2015 -- DeHon 72
Optimal Cover
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13 9 16 18 17
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Penn ESE535 Spring2015 -- DeHon 73
Optimal Cover
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13 9 16 18 17
Much better than 31!
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Penn ESE535 Spring2015 -- DeHon 74
Note
• There are nodes we cover that will not appear in final solution.
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Penn ESE535 Spring2015 -- DeHon 75
“Unused” Nodes
library
2 3 4 5 4 5
3
2
2
3
8
5 4
13 916 18 17
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Penn ESE535 Spring2015 -- DeHon 76
Dynamic Programming Solution
• Solution described is general instance of dynamic programming
• Require:– optimal solution to subproblems is optimal solution
to whole problem– (all optimal solutions equally good)– divide-and-conquer gets same (finite/small)
number of subproblems• Same technique used for instruction selection in code
generation for processors
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Penn ESE535 Spring2015 -- DeHon 77
Delay
• Similar– Delay(node) = Delay(gate)+Max(Delay(input))
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Penn ESE535 Spring2015 -- DeHon 78
DAG
• DAG = Directed Acyclic Graph– Distinguish from tree (tree DAG)– Distinguish from cyclic Graph– DAG Directed Graph (digraph)
tree DAG Digraph
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Penn ESE535 Spring2015 -- DeHon 79
Trees vs. DAGs
• Optimal for trees– why?
• Delay • Area
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Penn ESE535 Spring2015 -- DeHon 80
Not optimal for DAGs
• Why?
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Penn ESE535 Spring2015 -- DeHon 81
Not optimal for DAGs
• Why?
1+1+1=3
1+1+1=3
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Penn ESE535 Spring2015 -- DeHon 82
Not optimal for DAGs
• Why?
1+1+1=3
1+1+1=3 3+3+1=7 ?
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Penn ESE535 Spring2015 -- DeHon 83
Not Optimal for DAGs (area)
• Cost(N) = Cost(gate) + Cost(input nodes)
• think of sets• cost is magnitude of set union• Problem: minimum cost (magnitude) solution
isn’t necessarily the best pick– get interaction between subproblems– subproblem optimum not global...
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DAG Example
• Cover with 3 input gates
Penn ESE535 Spring2015 -- DeHon 84
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DAG Example
• Cover with 3 input gates
Penn ESE535 Spring2015 -- DeHon 85
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Penn ESE535 Spring2015 -- DeHon 86
Not Optimal for DAGs
• Delay:– in fanout model, depends on problem you
haven’t already solved (delay of node depends on number of uses)
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Penn ESE535 Spring2015 -- DeHon 87
What do people do?
• Cut DAGs at fanout nodes• optimally solve resulting trees
• Area– guarantees covered once
• get accurate costs in covering trees, made “premature” assignment of nodes to trees
• Delay – know where fanout is
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Penn ESE535 Spring2015 -- DeHon 88
Bounding
• Tree solution give bounds (esp. for delay)– single path, optimal covering for delay– (also make tree by replicating nodes at fanout
points)
• no fanout cost give lower bounds– know you can’t do better
• delay lower bounds useful, too– know what you’re giving up for area– when delay matters
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Penn ESE535 Spring2015 -- DeHon 89
(Multiple Objectives?)
• Like to say, get delay, then area– won’t get minimum area for that delay– algorithm only keep best delay– …but best delay on off critical path piece
not matter• …could have accepted more delay there
– don’t know if on critical path while building subtree
– (iterate, keep multiple solutions)
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Penn ESE535 Spring2015 -- DeHon 90
Many more details...
• Implement well
• Combine criteria
• …but now you know the main idea
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Penn ESE535 Spring2015 -- DeHon 91
Big Ideas
• simple cost models• problem formulation• identifying structure in the problem• special structure• characteristics that make problems hard• bounding solutions
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Penn ESE535 Spring2015 -- DeHon 92
Admin
• Reading for today: canvas• Reading for Wednesday:
– online/ACM DL– Highly relevant to assignment 3..6
• Office Hour: T4:30pm– Or make an appointment