A Unified Framework for Schedule and Storage Optimization William - PowerPoint PPT Presentation

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? i j

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? ??? i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � θ (i, j) is between: θ (i, j) = 2 ∗ i + j (inclusive) θ (i, j) = i (exclusive) i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � θ (i, j) is between: θ (i, j) = 2 ∗ i + j (inclusive) θ (i, j) = i (exclusive) i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � θ (i, j) is between: θ (i, j) = 2 ∗ i + j (inclusive) θ (i, j) = i (exclusive) i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � θ (i, j) is between: θ (i, j) = 2 ∗ i + j (inclusive) θ (i, j) = i (exclusive) i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � θ (i, j) is between: θ (i, j) = 2 ∗ i + j (inclusive) θ (i, j) = i (exclusive) i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � θ (i, j) is between: θ (i, j) = 2 ∗ i + j (inclusive) θ (i, j) = i (exclusive) i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � θ (i, j) is between: θ (i, j) = 2 ∗ i + j (inclusive) θ (i, j) = i (exclusive) i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j

Answering Question #3 • What is the shortest v that is valid for all legal affine schedules? i j

Answering Question #3 • What is the shortest v that is valid for all legal affine schedules? � Range of legal θ i j

Answering Question #3 • What is the shortest v that is valid for all legal affine schedules? � Range of legal θ i j

Answering Question #3 • What is the shortest v that is valid for all legal affine schedules? � Range of legal θ i j

Answering Question #3 • What is the shortest v that is valid for all legal affine schedules? � Range of legal θ i j

Answering Question #3 • What is the shortest v that is valid for all legal affine schedules? � Range of legal θ i j

Answering Question #3 • What is the shortest v that is valid for all legal affine schedules? � Range of legal θ i j