Faster Algorithms for Distance Sensitivity Oracles
Description: Faster Algorithms for Distance Sensitivity Oracles 1 14 Distance Sensitivity Oracles (DSOs) 2 14 Previous Work We consider unweighted graphs in this talk, for simplicity. Our results extend to graphs with small positive integer weights.
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slide1. Faster Algorithms for Distance Sensitivity Oracles 1 / 14<br>
slide2. Distance Sensitivity Oracles (DSOs) 2 / 14<br>
slide3. Previous Work We consider unweighted graphs in this talk, for simplicity.
Our results extend to graphs with small positive integer weights. 3 / 14<br>
slide4. Previous Work via Fast Matrix Mult? 4 / 14<br>
slide5. Our Results 5 / 14<br>
slide6. Bootstrapping DSOs A byproduct of [BK’09]! 6 / 14 Using the slower DSO Proof of Bootstrapping Thm The [BK’09] prep. algorithm Question: any other data structure problem where we could “unify” preprocessing and query time?<br>
slide7. 7 / 14<br>
slide8. Putting It Together 8 / 14 Using rect. mat. mul. Hitting set Bootstrapping Hitting set Bootstrapping Hitting set Hitting set Bootstrapping tradeoff<br>
slide9. 9 / 14<br>
slide10. 10 / 14<br>
slide11. Handling a Vertex Failure 11 / 14<br>
slide12. 12 / 14 Can be accelerated by fast rectangular mat. mult.!<br>
slide13. Wrap Up 13 / 14 Using rect. mat. mul. Hitting set Bootstrapping Hitting set Bootstrapping Hitting set Hitting set Bootstrapping tradeoff<br>
slide14. Further Directions 14 / 14<br>
slide15. Thank you! Questions are welcome! <br>
slide2. Distance Sensitivity Oracles (DSOs) 2 / 14<br>
slide3. Previous Work We consider unweighted graphs in this talk, for simplicity.
Our results extend to graphs with small positive integer weights. 3 / 14<br>
slide4. Previous Work via Fast Matrix Mult? 4 / 14<br>
slide5. Our Results 5 / 14<br>
slide6. Bootstrapping DSOs A byproduct of [BK’09]! 6 / 14 Using the slower DSO Proof of Bootstrapping Thm The [BK’09] prep. algorithm Question: any other data structure problem where we could “unify” preprocessing and query time?<br>
slide7. 7 / 14<br>
slide8. Putting It Together 8 / 14 Using rect. mat. mul. Hitting set Bootstrapping Hitting set Bootstrapping Hitting set Hitting set Bootstrapping tradeoff<br>
slide9. 9 / 14<br>
slide10. 10 / 14<br>
slide11. Handling a Vertex Failure 11 / 14<br>
slide12. 12 / 14 Can be accelerated by fast rectangular mat. mult.!<br>
slide13. Wrap Up 13 / 14 Using rect. mat. mul. Hitting set Bootstrapping Hitting set Bootstrapping Hitting set Hitting set Bootstrapping tradeoff<br>
slide14. Further Directions 14 / 14<br>
slide15. Thank you! Questions are welcome! <br>