Hanlin Ren, IIIS, Tsinghua University Joint work
Description: Hanlin Ren, IIIS, Tsinghua University Joint work with Yong Gu 1 15 Distance Sensitivity Oracles (DSOs) 2 15 Previous Work We consider unweighted graphs in this talk, for simplicity. Our results extend to graphs with small positive
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slide1. Hanlin Ren, IIIS, Tsinghua University
Joint work with Yong Gu 1 / 15<br>
slide2. Distance Sensitivity Oracles (DSOs) 2 / 15<br>
slide3. Previous Work We consider unweighted graphs in this talk, for simplicity.
Our results extend to graphs with small positive integer weights. 3 / 15<br>
slide4. Previous Work via Fast Matrix Mult? 4 / 15<br>
slide5. Preprocessing time of previous DSOs:
Other problems solvable by FMM have seen progress: Algorithm Preprocessing time Grandoni-Williams’12* Chechik-Cohen’20 Ren’20 5 / 15<br>
slide6. Our Result 6 / 15<br>
slide7. (Normal) DSO (Normal) DSO Implicit in [Ren’20] 7 / 15<br>
slide8. Symbolic Adjacency Matrix 8 / 15<br>
slide9. 9 / 15<br>
slide10. Handling a Vertex Failure 10 / 15<br>
slide11. 11 / 15<br>
slide12. Summary (Normal) DSO 12 / 15<br>
slide13. Unique & Consistent Shortest Paths × √ 13 / 15<br>
slide14. Unique & Consistent Shortest Paths Other applications of this besides DSO? 14 / 15<br>
slide15. Further Directions 15 / 15<br>
slide16. Thank you!<br>
Joint work with Yong Gu 1 / 15<br>
slide2. Distance Sensitivity Oracles (DSOs) 2 / 15<br>
slide3. Previous Work We consider unweighted graphs in this talk, for simplicity.
Our results extend to graphs with small positive integer weights. 3 / 15<br>
slide4. Previous Work via Fast Matrix Mult? 4 / 15<br>
slide5. Preprocessing time of previous DSOs:
Other problems solvable by FMM have seen progress: Algorithm Preprocessing time Grandoni-Williams’12* Chechik-Cohen’20 Ren’20 5 / 15<br>
slide6. Our Result 6 / 15<br>
slide7. (Normal) DSO (Normal) DSO Implicit in [Ren’20] 7 / 15<br>
slide8. Symbolic Adjacency Matrix 8 / 15<br>
slide9. 9 / 15<br>
slide10. Handling a Vertex Failure 10 / 15<br>
slide11. 11 / 15<br>
slide12. Summary (Normal) DSO 12 / 15<br>
slide13. Unique & Consistent Shortest Paths × √ 13 / 15<br>
slide14. Unique & Consistent Shortest Paths Other applications of this besides DSO? 14 / 15<br>
slide15. Further Directions 15 / 15<br>
slide16. Thank you!<br>