-
1
-
-
51249184131
-
Sorting in c log n parallel steps
-
M. Ajtai, J. Komlós, and E. Szemerédi. Sorting in c log n parallel steps. Combinatorica, 3(1):1-19, 1983.
-
(1983)
Combinatorica
, vol.3
, Issue.1
, pp. 1-19
-
-
Ajtai, M.1
Komlós, J.2
Szemerédi, E.3
-
2
-
-
51249173340
-
Eigenvalues and expanders
-
N. Alon. Eigenvalues and expanders. Combinatorica, 6(2):83-96, 1986.
-
(1986)
Combinatorica
, vol.6
, Issue.2
, pp. 83-96
-
-
Alon, N.1
-
3
-
-
38249033599
-
Better expanders and superconcentrators
-
N. Alon, Z. Galil, and V. D. Milman. Better expanders and superconcentrators. Journal of Algorithms, 8(3):337-347, 1987.
-
(1987)
Journal of Algorithms
, vol.8
, Issue.3
, pp. 337-347
-
-
Alon, N.1
Galil, Z.2
Milman, V.D.3
-
4
-
-
0035181247
-
Semi-direct product in groups and zig-zag product in graphs: Connections and applications
-
IEEE Computer Soc., Los Alamitos, CA
-
N. Alon, A. Lubotzky, and A. Wigderson. Semi-direct product in groups and zig-zag product in graphs: connections and applications (extended abstract). In 42nd IEEE Symposium on Foundations of Computer Science (Las Vegas, NV, 2001), pages 630-637. IEEE Computer Soc., Los Alamitos, CA, 2001.
-
(2001)
42nd IEEE Symposium on Foundations of Computer Science (Las Vegas, NV, 2001)
, pp. 630-637
-
-
Alon, N.1
Lubotzky, A.2
Wigderson, A.3
-
5
-
-
33750994100
-
1, Isoperimetric inequalities for graphs, and superconcentrators
-
1, isoperimetric inequalities for graphs, and superconcentrators. Journal of Combinatorial Theory. Series B, 38(1):73-88, 1985.
-
(1985)
Journal of Combinatorial Theory. Series B
, vol.38
, Issue.1
, pp. 73-88
-
-
Alon, N.1
Milman, V.D.2
-
7
-
-
0025535126
-
On the diameter of finite groups
-
IEEE Comput. Soc. Press. Los Alamitos, CA
-
L. Babai, G. Hetyei, W. M. Kantor, A. Lubotzky, and A. Seress. On the diameter of finite groups. In 31st Annual Symposium on Foundations of Computer Science, Vol. I, II (St. Louis, MO, 1990), pages 857-865. IEEE Comput. Soc. Press. Los Alamitos, CA. 1990.
-
(1990)
31st Annual Symposium on Foundations of Computer Science, Vol. I, II (St. Louis, MO, 1990)
, vol.1
, pp. 857-865
-
-
Babai, L.1
Hetyei, G.2
Kantor, W.M.3
Lubotzky, A.4
Seress, A.5
-
8
-
-
0038784507
-
Randomness-efficient low degree tests and short peps via epsilon-biased sets
-
ACM Press
-
E. Ben-Sasson, M. Sudan, S. Vadhan, and A. Wigderson. Randomness-efficient low degree tests and short peps via epsilon-biased sets. In Proceedings of the thirty-fifth ACM symposium on Theory of computing, pages 612-621. ACM Press, 2003.
-
(2003)
Proceedings of the Thirty-fifth ACM Symposium on Theory of Computing
, pp. 612-621
-
-
Ben-Sasson, E.1
Sudan, M.2
Vadhan, S.3
Wigderson, A.4
-
9
-
-
0036041924
-
Randomness conductors and constant-degree lossless expanders
-
ACM Press
-
M. Capalbo, O. Reingold, S. Vadhan, and A. Wigderson. Randomness conductors and constant-degree lossless expanders. In Proceedings of the thiry-fourth annual ACM symposium on Theory of computing, pages 659-668. ACM Press, 2002.
-
(2002)
Proceedings of the Thiry-fourth Annual ACM Symposium on Theory of Computing
, pp. 659-668
-
-
Capalbo, M.1
Reingold, O.2
Vadhan, S.3
Wigderson, A.4
-
10
-
-
0001891773
-
On the eigenvalues of random matrices
-
Studies in applied probability
-
P. Diaconis and M. Shahshahani. On the eigenvalues of random matrices. J. Appl. Probab., 31A:49-62, 1994. Studies in applied probability.
-
(1994)
J. Appl. Probab.
, vol.31 A
, pp. 49-62
-
-
Diaconis, P.1
Shahshahani, M.2
-
11
-
-
0000660463
-
The probability of generating the symmetric group
-
J. D. Dixon. The probability of generating the symmetric group. Math. Z., 110:199-205, 1969.
-
(1969)
Math. Z.
, vol.110
, pp. 199-205
-
-
Dixon, J.D.1
-
12
-
-
0001152232
-
Quaternäre quadratische Formen und die Riemannsche Vermutung für die Kongruenzzetafunktion
-
M. Eichler. Quaternäre quadratische Formen und die Riemannsche Vermutung für die Kongruenzzetafunktion. Arch. Math., 5:355-366, 1954.
-
(1954)
Arch. Math.
, vol.5
, pp. 355-366
-
-
Eichler, M.1
-
13
-
-
0000871697
-
Explicit constructions of linear-sized superconcentrators
-
June
-
O. Gabber and Z. Galil. Explicit constructions of linear-sized superconcentrators. J. Comput. Syst. Sci., 22(3):407-420, June 1981.
-
(1981)
J. Comput. Syst. Sci.
, vol.22
, Issue.3
, pp. 407-420
-
-
Gabber, O.1
Galil, Z.2
-
14
-
-
0025742358
-
Security preserving amplification of hardness
-
St. Louis, Missouri, 22-24 Oct. IEEE
-
O. Goldreich, R. Impagliazzo, L. Levin, R. Venkatesan. and D. Zuckerman, Security preserving amplification of hardness. In 31st Annual Symposium on Foundations of Computer Science, volume I, pages 318-326, St. Louis, Missouri, 22-24 Oct. 1990. IEEE.
-
(1990)
31st Annual Symposium on Foundations of Computer Science
, vol.1
, pp. 318-326
-
-
Goldreich, O.1
Impagliazzo, R.2
Levin, L.3
Venkatesan, R.4
Zuckerman, D.5
-
15
-
-
0002302520
-
Spaces and questions
-
Part I of Special Volume on GAFA 2000 (Tel Aviv, 1999)
-
M. Gromov. Spaces and questions. Geometric and Functional Analysis, pages 118-161, 2000. Part I of Special Volume on GAFA 2000 (Tel Aviv, 1999).
-
(2000)
Geometric and Functional Analysis
, pp. 118-161
-
-
Gromov, M.1
-
16
-
-
0028022375
-
Pseudorandomness for network algorithms
-
Montréal, Québec, Canada, 23-25 May
-
R. Impagliazzo, N. Nisan, and A. Wigderson. Pseudorandomness for network algorithms. In Proceedings of the Twenty-Sixth Annual ACM Symposium on the Theory of Computing, pages 356-364, Montréal, Québec, Canada, 23-25 May 1994.
-
(1994)
Proceedings of the Twenty-sixth Annual ACM Symposium on the Theory of Computing
, pp. 356-364
-
-
Impagliazzo, R.1
Nisan, N.2
Wigderson, A.3
-
18
-
-
51249173945
-
Expanders obtained from affine transformations
-
S. Jimbo and A. Maruoka. Expanders obtained from affine transformations. Combinatorica, 7(4):343-355, 1987.
-
(1987)
Combinatorica
, vol.7
, Issue.4
, pp. 343-355
-
-
Jimbo, S.1
Maruoka, A.2
-
20
-
-
34250526463
-
On the connection of the dual space of a group with the structure of its closed subgroups
-
D. Kazhdan. On the connection of the dual space of a group with the structure of its closed subgroups (russian). Funkcional. Anal. i Prilozh., 1:71-74, 1967.
-
(1967)
Funkcional. Anal. i Prilozh.
, vol.1
, pp. 71-74
-
-
Kazhdan, D.1
-
21
-
-
0021372575
-
Limitations on explicit constructions of expanding graphs
-
M. Klawe. Limitations on explicit constructions of expanding graphs. SIAM J. Comput., 13(1):156-166, 1984.
-
(1984)
SIAM J. Comput.
, vol.13
, Issue.1
, pp. 156-166
-
-
Klawe, M.1
-
22
-
-
0001056702
-
The probability of generating a finite simple group
-
M. W. Liebeck and A. Shalev. The probability of generating a finite simple group. Geom. Dedicata, 56(1):103-113, 1995.
-
(1995)
Geom. Dedicata
, vol.56
, Issue.1
, pp. 103-113
-
-
Liebeck, M.W.1
Shalev, A.2
-
23
-
-
0242337473
-
Mixing times
-
Amer. Math. Soc., Providence, RI
-
L. Lovász and P. Winkler. Mixing times. In Microsurveys in discrete probability (Princeton, NJ, 1997), volume 41 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., pages 85-133. Amer. Math. Soc., Providence, RI. 1998.
-
(1998)
Microsurveys in Discrete Probability (Princeton, NJ, 1997), Volume 41 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci.
, vol.41
, pp. 85-133
-
-
Lovász, L.1
Winkler, P.2
-
25
-
-
0035581584
-
The product replacement algorithm and Kazhdan's property
-
electronic
-
A. Lubotzky and I. Pak. The product replacement algorithm and Kazhdan's property (T). Journal of the American Mathematical Society, 14(2):347-363 (electronic), 2001.
-
(2001)
Journal of the American Mathematical Society
, vol.14
, Issue.2
, pp. 347-363
-
-
Lubotzky, A.1
Pak, I.2
-
26
-
-
0000848816
-
Ramanujan graphs
-
A. Lubotzky, R. Phillips, and P. Sarnak. Ramanujan graphs. Combinatorica, 8(3):261-277, 1988.
-
(1988)
Combinatorica
, vol.8
, Issue.3
, pp. 261-277
-
-
Lubotzky, A.1
Phillips, R.2
Sarnak, P.3
-
27
-
-
0037906726
-
Groups and expanders
-
Amer. Math. Soc., Providence, RI
-
A. Lubotzky and B. Weiss. Groups and expanders. In Expanding graphs (Princeton, NJ, 1992), volume 10 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., pages 95-109. Amer. Math. Soc., Providence, RI, 1993.
-
(1993)
Expanding Graphs (Princeton, NJ, 1992), Volume 10 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci.
, vol.10
, pp. 95-109
-
-
Lubotzky, A.1
Weiss, B.2
-
28
-
-
0000789645
-
Explicit constructions of expanders
-
G. A. Margulis. Explicit constructions of expanders. Problemy Peredači Informacii, 9(4):71-80, 1973.
-
(1973)
Problemy Peredači Informacii
, vol.9
, Issue.4
, pp. 71-80
-
-
Margulis, G.A.1
-
29
-
-
0003059022
-
Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators
-
G. A. Margulis. Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators. Problemy Peredachi Informatsii, 24(1):51-60, 1988.
-
(1988)
Problemy Peredachi Informatsii
, vol.24
, Issue.1
, pp. 51-60
-
-
Margulis, G.A.1
-
31
-
-
0002622843
-
Existence and explicit constructions of 9 + 1 regular Ramanujan graphs for every prime power q
-
M. Morgenstern. Existence and explicit constructions of 9 + 1 regular Ramanujan graphs for every prime power q. Journal of Combinatorial Theory. Series B, 62(1):44-62. 1994.
-
(1994)
Journal of Combinatorial Theory. Series B
, vol.62
, Issue.1
, pp. 44-62
-
-
Morgenstern, M.1
-
32
-
-
0027641832
-
Small-bias probability spaces: Efficient constructions and applications
-
Aug.
-
J. Naor and M. Naor. Small-bias probability spaces: Efficient constructions and applications. SIAM J. Comput., 22(4):838-856, Aug. 1993.
-
(1993)
SIAM J. Comput.
, vol.22
, Issue.4
, pp. 838-856
-
-
Naor, J.1
Naor, M.2
-
34
-
-
84968516156
-
Some remarks on commutators
-
O. Ore. Some remarks on commutators. Proc. Amer. Math. Soc., 2:307-314, 1951.
-
(1951)
Proc. Amer. Math. Soc.
, vol.2
, pp. 307-314
-
-
Ore, O.1
-
35
-
-
0002550078
-
On the complexity of a concentrator
-
Stockholm
-
M. S. Pinsker. On the complexity of a concentrator. In 7th Annual Teletraffic Conference, pages 318/1-318/4, Stockholm, 1973.
-
(1973)
7th Annual Teletraffic Conference
-
-
Pinsker, M.S.1
-
36
-
-
0023580443
-
Sorting and selecting in rounds
-
Dec.
-
N. Pippenger. Sorting and selecting in rounds. SIAM J. Comput., 16(6): 1032-1038, Dec. 1987.
-
(1987)
SIAM J. Comput.
, vol.16
, Issue.6
, pp. 1032-1038
-
-
Pippenger, N.1
-
38
-
-
0036000527
-
Entropy waves, the zig-zag graph product, and new constant-degree expanders
-
O. Reingold, S. Vadhan, and A. Wigderson. Entropy waves, the zig-zag graph product, and new constant-degree expanders. Ann. of Math. (2), 155(1):157-187, 2002.
-
(2002)
Ann. of Math. (2)
, vol.155
, Issue.1
, pp. 157-187
-
-
Reingold, O.1
Vadhan, S.2
Wigderson, A.3
-
39
-
-
0002739011
-
On the estimation of Fourier coefficients of modular forms
-
Amer. Math. Soc., Providence, R.I.
-
A. Selberg. On the estimation of Fourier coefficients of modular forms. In Proc. Sympos. Pure Math., Vol. VIII, pages 1-15. Amer. Math. Soc., Providence, R.I., 1965.
-
(1965)
Proc. Sympos. Pure Math.
, vol.8
, pp. 1-15
-
-
Selberg, A.1
-
40
-
-
0024019629
-
Expanders, randomness, or time versus space
-
June
-
M. Sipser. Expanders, randomness, or time versus space. J. Comput. Syst. Sci., 36(3):379-383, June 1988.
-
(1988)
J. Comput. Syst. Sci.
, vol.36
, Issue.3
, pp. 379-383
-
-
Sipser, M.1
-
42
-
-
0030283874
-
Linear-time encodable and decodable error-correcting codes
-
D. A. Spielman. Linear-time encodable and decodable error-correcting codes. IEEE Transactions on Information Theory, 42(6, part 1):1723-1731, 1996.
-
(1996)
IEEE Transactions on Information Theory
, vol.42
, Issue.6 PART 1
, pp. 1723-1731
-
-
Spielman, D.A.1
-
43
-
-
0000472681
-
Explicit concentrators from generalized n-gons
-
M. R. Tanner. Explicit concentrators from generalized n-gons. SIAM Journal on Algebraic Discrete Methods, 5(3):287-293, 1984.
-
(1984)
SIAM Journal on Algebraic Discrete Methods
, vol.5
, Issue.3
, pp. 287-293
-
-
Tanner, M.R.1
-
45
-
-
85016972944
-
Graph-theoretic arguments in low-level complexity
-
Lecture Notes in Comput. Sci., Springer, Berlin
-
L. G. Valiant. Graph-theoretic arguments in low-level complexity. In Mathematical foundations of computer science (Proc. Sixth Sympos., Tatranská Lomnica, 1977), pages 162-176. Lecture Notes in Comput. Sci., Vol. 53. Springer, Berlin, 1977.
-
(1977)
Mathematical Foundations of Computer Science (Proc. Sixth Sympos., Tatranská Lomnica, 1977)
, vol.53
, pp. 162-176
-
-
Valiant, L.G.1
-
46
-
-
0040707391
-
Expanders that beat the eigenvalue bound: Explicit construction and applications
-
A. Wigderson and D. Zuckerman. Expanders that beat the eigenvalue bound: explicit construction and applications. Combinatorica, 19(1):125-138, 1999.
-
(1999)
Combinatorica
, vol.19
, Issue.1
, pp. 125-138
-
-
Wigderson, A.1
Zuckerman, D.2
|