Research

Papers, Surveys, Notes

1. Dvoretzky-type theorem for Ahlfors regular spaces. M. Mendel. Studia Mathematica 268 (2023), 1-22.  arXiv:2106.11737 

2. A simple proof of Dvoretzky-type theorem for Hausdorff dimension in doubling spaces. M. Mendel,  Analysis and Geometry in Metric Spaces 10 (2022), 50-62.  arXiv:2104.11944

3. Reliable Spanners for Metric Spaces. S. Har-Peled, M. Mendel, and D. Olah, ACM Trans. Algo. 19(1) 1–27 (2023), arXiv:2007.08738, SoCG 2021

4. Nonpositive curvature is not coarsely universal. A. Eskenazis, M. Mendel, and A. Naor. Invent. Math. 217 (2019), no. 3, 833–886 (or this link). arXiv:1808.02179.  

5. A simple proof of Johnson-Lindenstrauss extension. M. Mendel.  American Mathematical Monthly 126 (2019) no. 9,  838-840. arXiv:1803.03606

6. A relation between finitary Lipschitz extension moduli. M. Mendel and A. Naor, 2017. arXiv:1707.07289

7. Expanders with respect to Hadamard spaces and random graphs. M. Mendel and A. Naor. Duke Math. J. 164, no. 8, 1471–1548, 2015, ITCS '14, arXiv:1306.5434.

8. Spectral calculus and Lipschitz extension for barycentric metric spaces. M. Mendel and A.Naor. Analysis and Geometry in Metric Spaces, 1, 2013 163-199, arXiv:1301.3963.

9. A node-capacitated Okamura-Seymour theorem. J. R. Lee, M. Mendel and M. Moharrami. Mathematical programming, Series A., 2014,  STOC '13, arXiv:1209.2744.

10. On the Hausdorff dimension of ultrametric subsets in Rn. J. R. Lee, M. Mendel and M. Moharrami. Fund. Math. 218, 285-290, 2012,. arXiv:1205.2094

11. Ultrametric skeletons. M. Mendel and A. Naor. Proc. of the National Academy of Sci. 110(48): 19256-19262,  2013,   arXiv:1112.3416.

12. A note on extensions of approximate ultrametrics. M. Mendel, 2012. arXiv:1211.3041

13. Ultrametric subsets with large Hausdorff dimension. M. Mendel and A.Naor, Inventiones mathematicae 192(1): 1-54, 2013, arXiv:1106.0879

14. Improved bounds in the metric cotype inequality for Banach spaces, O. Giladi, M. Mendel, and A. Naor. Journal of Functional Analysis 260, 164–194, 2011, arXiv:1003:0279

15. Nonlinear spectral calculus and super-expanders M. Mendel, and A. Naor. Publications mathématiques de l'IHÉS 119 (2014) no. 1, 1-95. arXiv:1207.4705, SODA '10  

16. A note on dichotomies for metric transforms. M. Mendel  and A.Naor, 2011. arXiv:1102.1800

17. Fast C-K-R Partitions of Sparse Graphs, M. Mendel, and C. Schwob, Chicago J. Theoretical Comp. Sci., 2009(2), arXiv:0809.1902

18. Markov convexity and local rigidity of distorted metrics, M. Mendel, and A. Naor. J. European Math. Soc. 15(1):287-337, 2013. arXiv:0803.1697, SoCG '08

19. Metrical task systems M. Mendel. In  Encyclopedia of Algorithms, edited by M.-Y. Kao. 2008. (pdf)

20. Metric dichotomies M. Mendel. In G.N. Arzhantseva, A.Valette (eds.), Limits of graphs in group theory and computer science, EPFL Press, 2009  arXiv:0710.1994

21. Maximum gradient embedding and monotone clustering, M. Mendel, and A. Naor. Combinatorica 30(5): 581-615, 2010 arxiv:cs.DS/0606109  APPROX '07   

22. Ramsey partitions and proximity data structures M. Mendel, and A. Naor. J. European Math. Soc. 9(2): 253-275, 2007,  arXiv:cs.DS/0511084  FOCS '06

23. Scaled Enflo type is equivalent to Rademacher type M. Mendel, and A. Naor, Bull. London Math. Soc. 39(3):493-498, 2007 arXiv:math.FA/0506215

24. Metric cotype, M. Mendel, and A. Naor. Ann. of Math. 168(1), 247-298 (2008), arXiv:math.FA/0506201, SODA '06

25. Some applications of Ball's extension theorem, M. Mendel, and A. Naor. Proc. Amer. Math. Soc. 134: 2577-2584, 2006 (pdf)

26. Fast construction of nets in low dimensional metrics, and their applications, S. Har-Peled, and M. Mendel. SIAM J. Comput. 35(5):1148-1184, 2006, arXiv:cs.DS/0409057, SoCG '05

27. Measured descent: A new embedding method for finite metric spaces, R. Krauthgamer, J. R. Lee, M. Mendel, and A. Naor. Geom. Funct. Anal. 15(4):839-858, 2005, arXiv:cs.DS/0412008, FOCS '04 

28. Metric structures in L1: Dimension, snowflakes, and average distortion, J. R. Lee, M. Mendel, and A. Naor. European J. Combin. 26(8): 1180-1190,2005, arXiv:math.MG/0407278, LATIN '04

29. Euclidean quotients of finite metric spaces, M. Mendel, and A. Naor. Adv. Math. 189(2) 451-494, 2004, arXiv:math.MG/0406349

30. On metric Ramsey-type phenomena, Y. Bartal, N. Linial, M. Mendel, and A. Naor. Ann. of Math. 162(2): 643-709, 2005, arXiv:math.MG/0406353, STOC '03

31. Limitations to Frechet metric embedding method, Y. Bartal, N. Linial, M. Mendel, and A. Naor. Israel J. Math. 151: 111-124, 2006, arXiv:math.MG/0406404

32. On metric Ramsey-type dichotomies, Y. Bartal, N. Linial, M. Mendel, and A. Naor. J. London Math. Soc. 71(2): 289-303, 2005, arXiv:math.CO/0406374

33. Some low distortion metric Ramsey problems, Y. Bartal, N. Linial, M. Mendel, and A. Naor. Discrete Comput. Geom. 33(1): 25-41, 2005, arXiv:math.MG/0406358

34. Dimension reduction for ultrametrics, Y. Bartal, and M. Mendel. SODA '04 (pdf)

35. Multi-embedding of metric spaces, Y. Bartal, and M. Mendel. SIAM J. Comput. 34(1): 248-259, 2004, arXiv:cs.DS/0408003, SODA '03

36. Online companion caching, A. Fiat, M. Mendel, and S. S. Seiden. Theoret. Comput. Sci. 324(2-3): 183-200, 2004, arXiv:cs.DS/0406036, ESA '02

37. Online algorithms for paging and metrical task systems. M. Mendel Ph.D. thesis, Tel-Aviv University, 2002. (pdf)

38. Ramsey-type Theorems for Metric Spaces with Applications to Online Problems, Y. Bartal, B. Bollobas, and M. Mendel. J. Comput. System Sci. 72(5):890-921, 2006, arXiv:cs.DS/0406028, FOCS '01

39. Better algorithms for unfair metrical task systems and applications, A. Fiat, and M. Mendel. SIAM J. Comput. 32(6):1403-1422, 2003, arXiv:cs.DS/0406034, STOC '00

40. Truly online paging with locality of reference, A. Fiat, and M. Mendel. arXiv:cs.DS/0601127, FOCS '97 

Withdrwan

Randomized k-server algorithms for growth-rate bounded graphs, Withdrawal announcement, SODA '04, and J. Algorithms 55(2) 192-202, 2005. [arXiv:cs.DS/0406033]

Coauthors

Yair Bartal, Bela Bollobas, Alexandros Eskenazis, Amos Fiat, Ohad Giladi,  Sariel Har-Peled, Robert Krauthgamer, James R. Lee, Mohammad Moharrami, Nathan Linial, Assaf Naor,  Dániel Oláh, Chaya Schowb, Steven S. Seiden

Online listing

arXiv DBLP  MathSciNet  Google Scholar  ORCiD

Research interests

Algorithms and geometry in discrete metric spaces, metric geometry,  nonlinear geometry of Banach spaces, optimization algorithms, data structures, online algorithms.

Presentations

here