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r t r r s t s s rst r

  1. ❆ ✉♥✐✜❡❞ ❛♣♣r♦❛❝❤ t♦ ❧✐♥❡❛r ♣r♦❜✐♥❣ ❤❛s❤✐♥❣ ❙✈❛♥t❡ ❏❛♥s♦♥ ❯♣♣s❛❧❛ ❯♥✐✈❡rs✐t② ❆❧❢r❡❞♦ ❱✐♦❧❛ ❯♥✐✈❡rs✐❞❛❞ ❞❡ ❧❛ ❘❡♣ú❜❧✐❝❛ ❆♦❢❆ ✷✵✶✹ ❉❡❞✐❝❛t❡❞ t♦ P❤✐❧✐♣♣❡ ❋❧❛❥♦❧❡t

  2. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  3. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  4. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  5. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  6. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  7. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  8. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  9. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  10. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  11. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  12. ❚❤❡ ♣r♦❜❧❡♠✳ ❚❤❡ t❛❜❧❡ ❤❛s ♠ ♣❧❛❝❡s ♦❢ ❝❛♣❛❝✐t② ❜ t♦ ❤❛s❤ ✭♣❛r❦✮ ❢r♦♠ ✵ t♦ ♠ � ✶ ✱ ❛♥❞ ♥ ✐♥s❡rt❡❞ ❡❧❡♠❡♥ts ✭❝❛rs✮✳ ❊❛❝❤ ❡❧❡♠❡♥t ✐s ❣✐✈❡♥ ❛ ❤❛s❤ ✈❛❧✉❡ ✭♣r❡❢❡rr❡❞ ♣❛r❦✐♥❣ ❧♦t✮✳ ■❢ ♣❧❛❝❡ ✐s ♥♦t ❢✉❧❧✱ t❤❡♥ t❤❡ ❡❧❡♠❡♥t ✐s st♦r❡❞ t❤❡r❡✳ ❖t❤❡r✇✐s❡✱ ❧♦♦❦s s❡q✉❡♥t✐❛❧❧② ❢♦r ❛♥ ❡♠♣t② ♣❧❛❝❡✳ ■❢ ♥♦ ❡♠♣t② ♣❧❛❝❡ ✉♣ t♦ t❤❡ ❡♥❞ ♦❢ t❤❡ t❛❜❧❡✱ t❤❡ s❡❛r❝❤ ❢♦❧❧♦✇s ❛t ❧♦❝❛t✐♦♥ ✵✳ ❙❡✈❡r❛❧ ❘✳❱✳ t♦ st✉❞②✱ ♠❛✐♥❧② r❡❧❛t❡❞ ✇✐t❤ ❝♦st ♦❢ ✐♥❞✐✈✐❞✉❛❧ s❡❛r❝❤❡s ❛♥❞ t♦t❛❧ ❝♦♥str✉❝t✐♦♥ ❝♦st✳ ❱❡r② ✐♠♣♦rt❛♥t s♣❡❝✐❛❧ ❝❛s❡✿ P❛r❦✐♥❣ Pr♦❜❧❡♠ ✳ ■♥ ♣❛r❦✐♥❣ t❤❡ ❝❛r ✐s ❧♦st ✐❢ ♥♦ ❛✈❛✐❧❛❜❧❡ ♣❧❛❝❡ t♦ ♣❛r❦ ✉♣ t♦ t❤❡ ❡♥❞ ♦❢ t❤❡ t❛❜❧❡✳ ▼❛✐♥ ❘✳❱✳ ✐s t❤❡ ♥✉♠❜❡r ♦❢ ❧♦st ❝❛rs✳

  13. ▲✐♥❡❛r Pr♦❜✐♥❣ ❍❛s❤✐♥❣✳

  14. ❚❤❡ ♠❛t❤❡♠❛t✐❝❛❧ ❜❡❛✉t② ♦❢ ▲✐♥❡❛r Pr♦❜✐♥❣✦

  15. ✶✾✻✷✿ ❙✉♠♠❡r ✇♦r❦ ❜② ❉♦♥ ❑♥✉t❤ ✳✳✳

  16. ❖r✐❣✐♥❛❧ r❡s✉❧ts✳ ▲❡t ❛ ❤❛s❤ t❛❜❧❡ ✇✐t❤ ♠ ♣♦s✐t✐♦♥s ❛♥❞ ♥ ✐♥s❡rt❡❞ ❡❧❡♠❡♥ts✳ ▲❡t P ♠❀♥ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ t❤❡ ❧❛st ♣♦s✐t✐♦♥ ❜❡✐♥❣ ❡♠♣t②✳ � ✶ � ♥ ✁ P ♠❀♥ ❂ ✳ ♠ ▲❡t ❈ ♠❀♥ t❤❡ ❘✳❱✳ ❢♦r t❤❡ ♥✉♠❜❡r ♦❢ s✉❝❝❡ss❢✉❧ s❡❛r❝❤❡s ♦❢ ❛ r❛♥❞♦♠ ❡❧❡♠❡♥t✳ ❊ ❬ ❈ ♠❀♥ ❪ ❂ ✶ ✷ ✭✶ ✰ ◗ ✵ ✭✭ ♠❀ ♥ � ✶✮✮ ✳ ✏ ✑ ❊ ❬ ❈ ♠❀☛♠ ❪ ❂ ✶ ✶ ✶ ✰ ✇✐t❤ ✵ ✔ ☛ ❁ ✶ ✳ ✷ ✶ � ☛ ❊ ❬ ❈ ♥❀♥ ❪ ❂ ♣ ✙♥ ✽ ✰ ❖ ✭✶✮ ✭♣r♦✈❡❞ ♦♥ ♠❛② ✷✵✱ ✶✾✻✺✮✳ ▲❡t ❯ ♠❀♥ t❤❡ ❘✳❱✳ ❢♦r t❤❡ ♥✉♠❜❡r ♦❢ ✉♥s✉❝❝❡ss❢✉❧ s❡❛r❝❤❡s ♦❢ ❛ r❛♥❞♦♠ ❡❧❡♠❡♥t✳ ❊ ❬ ❯ ♠❀♥ ❪ ❂ ✶ ✷ ✭✶ ✰ ◗ ✶ ✭✭ ♠❀ ♥ � ✶✮✮ ✳ ✏ ✑ ❊ ❬ ❯ ♠❀☛♠ ❪ ❂ ✶ ✶ ✶ ✰ ✇✐t❤ ✵ ✔ ☛ ❁ ✶ ✳ ✷ ✭✶ � ☛ ✮ ✷ ❚❤❡ ❘❛♠❛♥✉❥❛♥ ◗ ❢✉♥❝t✐♦♥ ✐s t❤❡ s♣❡❝✐❛❧ ❝❛s❡ ◗ ✵ ✭ ♥❀ ♥ ✮ ♦❢ ♥ ✥ ✦ ♥ ❦ ❦ ✰ r ❳ ◗ r ✭ ♠❀ ♥ ✮ ❂ ♠ ♥ ✿ ❦ ❦ ❂✵

  17. ❚✇♦ ♠♦❞❡❧s t♦ ❛♥❛❧②③❡ t❤❡ ♣r♦❜❧❡♠✳ ❊①❛❝t ✜❧❧✐♥❣ ♠♦❞❡❧✳ ❆ ✜①❡❞ ♥✉♠❜❡r ♦❢ ❦❡②s ♥ ✱ ❛r❡ ❞✐str✐❜✉t❡❞ ❛♠♦♥❣ ♠ ❧♦❝❛t✐♦♥s✱ ❛♥❞ ❛❧❧ ♠ ♥ ♣♦ss✐❜❧❡ ❛rr❛♥❣❡♠❡♥ts ❛r❡ ❡q✉❛❧❧② ❧✐❦❡❧② t♦ ♦❝❝✉r✳ P♦✐ss♦♥ ♠♦❞❡❧✳ ❊❛❝❤ ❧♦❝❛t✐♦♥ r❡❝❡✐✈❡s ❛ ♥✉♠❜❡r ♦❢ ❦❡②s t❤❛t ✐s P♦✐ss♦♥ ❞✐str✐❜✉t❡❞ ✇✐t❤ ♣❛r❛♠❡t❡r ❜☛ ✱ ❛♥❞ ✐s ✐♥❞❡♣❡♥❞❡♥t ♦❢ t❤❡ ♥✉♠❜❡r ♦❢ ❦❡②s ❣♦✐♥❣ ❡❧s❡✇❤❡r❡✳ ❚❤✐s ✐♠♣❧✐❡s t❤❛t t❤❡ t♦t❛❧ ♥✉♠❜❡r ♦❢ ❦❡②s✱ ◆ ✱ ✐s ✐ts❡❧❢ ❛ P♦✐ss♦♥ ❞✐str✐❜✉t❡❞ r❛♥❞♦♠ ✈❛r✐❛❜❧❡ ✇✐t❤ ♣❛r❛♠❡t❡r ❜☛♠ ✿ Pr ❬ ◆ ❂ ♥ ❪ ❂ ❡ � ❜☛♠ ✭ ❜☛♠ ✮ ♥ ✿ ♥ ✦

  18. P♦✐ss♦♥ ❚r❛♥s❢♦r♠✳ ❘❡s✉❧ts ✐♥ ♦♥❡ ♠♦❞❡❧ ❝❛♥ ❜❡ tr❛♥s❢❡r❡❞ ✐♥t♦ t❤❡ ♦t❤❡r ♠♦❞❡❧ ❜② t❤❡ P♦✐ss♦♥ ❚r❛♥s❢♦r♠✿ ✭ ❜☛♠ ✮ ♥ ❳ Pr ❬ ◆ ❂ ♥ ❪ ❢ ♠❀♥ ❂ ❡ � ❜☛♠ ❳ P ♠ ❬ ❢ ♠❀♥ ❀ ❜☛ ❪ ❂ ❢ ♠❀♥ ✿ ♥ ✦ ♥ ✕ ✵ ♥ ✕ ✵ ■♥✈❡rs✐♦♥ ❚❤❡♦r❡♠✿ ❬●♦♥♥❡t ❛♥❞ ▼✉♥r♦ ✶✾✽✹❪ ♥ ❦ ❛ ♠❀❦ ✭ ❜♠☛ ✮ ❦ t❤❡♥ ❢ ♠❀♥ ❂ ❳ ❳ ■❢ P ♠ ❬ ❢ ♠❀♥ ❀ ❜☛ ❪ ❂ ❛ ♠❀❦ ✭ ❜♠ ✮ ❦ ✿ ❦ ✕ ✵ ❦ ✕ ✵ ❚❤❡ P♦✐ss♦♥ ♠♦❞❡❧ ✐s ❛♥ ❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ t❤❡ ❡①❛❝t ✜❧❧✐♥❣ ♠♦❞❡❧ ✇❤❡♥ ♥❀ ♠ ✦ ✶ ✇✐t❤ ♥❂♠ ❂ ❜☛ ✇✐t❤ ✵ ✔ ☛ ❁ ✶ ✳

  19. ▲✐♥❡❛r Pr♦❜✐♥❣ ❛♥❞ t❤❡ ❙②♠❜♦❧✐❝ ▼❡t❤♦❞ ✭■✮✳

  20. ▲✐♥❡❛r Pr♦❜✐♥❣ ❛♥❞ t❤❡ ❙②♠❜♦❧✐❝ ▼❡t❤♦❞ ✭■✮✳

  21. ❈♦♥❝❧✉s✐♦♥s ✭❑♥✉t❤✮✳

  22. ▲✐♥❡❛r Pr♦❜✐♥❣ ❛♥❞ t❤❡ ❙②♠❜♦❧✐❝ ▼❡t❤♦❞ ✭■■✮✳

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CSE 167: Problems on Curves Ravi Ramamoorthi Questions 1. Consider a quadratic B-spline curve with uniform knot spacing. Consider a segment with control points (1, 0) (1, 1) and (0, 1) in that order. What are the end-points of the curve segment?

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CS 401 Master Theorem / Closest Points Xiaorui Sun 1 Master Theorem Master Theorem % & +

CS 401 Master Theorem / Closest Points Xiaorui Sun 1 Master Theorem Master Theorem % & +

CS 401 Master Theorem / Closest Points Xiaorui Sun 1 Master Theorem Master Theorem % & + (" ) for all " > +. Then, Suppose ! " = $ ! c: absolute constant If $ < + ) then ! " = " ) If $ = + ) then

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