Office Hours for Spring 2014

Hosam M. Mahmoud

Hosam M. Mahmoud

Faculty: Full-Time
Address: Rome Hall
801 22nd St NW
Washington, DC, 20052
Phone: 202-994-6667

Areas of Expertise

Probabilistic analysis of algorithms, Random discrete structures, Analytic probability.


Professor of Statistics


Ph.D. in Computer Science, The Ohio State University, Columbus, Ohio, 1983.

M.S. in Computer Science, The Ohio State University, Columbus, Ohio, 1981.

B.Sc. in Mathematics, Cairo University, Egypt, 1979. Graduated with distinction with honors.

B.Sc. in Electrical Engineering, Cairo University, Egypt, 1976. Graduated with distinction with honors.



Mahmoud, H. and Pittel, B. (1984). On the most probable shape of a search tree grown from random permutations. SIAM Journal on Algebraic and Discrete methods, 1, 69-81.

Mahmoud, H. (1986). The expected distribution of node degrees in random binary search trees. The Computer Journal, 29, 36-37.

Mahmoud, H. (1986). On the average internal path length of m-ary search trees. ActaInformatica23, 111-117.

Gastwirth, J. and Mahmoud, H. (1986). An efficiency robust nonparametric test for scale change for data from a Gamma-distribution. Technometrics28, 81-84.

Mahmoud, H. and Pittel, B. (1988). On the joint distribution of the insertion path length and the number of comparisons in search trees. Discrete Applied Mathematics20, 243-251.

Mahmoud, H. and Pittel, B. (1989). Analysis of the space of search trees under the random insertion algorithm. Journal of Algorithms10, 52-75.

Mahmoud, H. (1991). Limiting distributions for path lengths in recursive trees. Probability in the Engineering and Informational Sciences5, 53-59.

Mahmoud, H. and Smythe, R. (1991). On the distribution of leaves in rooted subtrees of recursive trees. The Annals of Applied Probability1, 406-418.

Mahmoud, H. (1992). A law of large numbers for path lengths in search trees. Chapter inRandom Graphs: vol. II, A. Frieze and M. Karonski, Editors. Wiley, New York.

Mahmoud, H. (1992). Distances in random plane-oriented recursive trees. Journal of Computational Applied Mathematics, invited paper in the special volume on Asymptoticsin Discrete Mathematics and Analysis, 41, 237-245.

Mahmoud, H. and Smythe, R. (1992). Asymptotic joint normality of outdegrees of nodes in random recursive trees. Random Structures and Algorithms3, 255-266.

Mahmoud, H., Smythe, R. and Szymanski, J. (1993). On the structure of plane-oriented recursive trees and their branches. Random Structures and Algorithms4, 151-176.

Hurley, C. and Mahmoud, H. (1994). Analysis of an algorithm for random sampling.Probability in the Engineering and Informational Sciences8, 153-168.

Mahmoud, H. (1994). A strong law for the height of random binary pyramids. The Annals of Applied Probability4, 923-932.

Lew, L. and Mahmoud, H. (1994). The joint distribution of elastic buckets in multiwaysearch trees. SIAM Journal on Computing, 23, 1050-1074.

Smythe, R. and Mahmoud, H. (1994). A survey of recursive trees. Theorya Imovirnostyta Matemika Statystika51 (in Ukrainian), 1-29; an English translation appears in Theory of Probability and Its Applications (1996).

Mahmoud, H. (1995). The joint distribution of the three types of nodes in uniform binary trees. Algorithmica13, 313-323.

Mahmoud, H. and Orlandic, R. (1995). Toward a formal derivation of the expected behavior of prefix B-trees. Probability in the Engineering and Informational Sciences2, 183-192.

Mahmoud, H. and Smythe, R. (1995). Probabilistic analysis of bucket recursive trees.Theoretical Computer Science, a special volume on the analysis of algorithms, 144, 221-249.

Mahmoud, H., Modarres, R. and Smyhe, R. (1995). Analysis of QUICKSELECT: An algorithm for order statistics. Theoretical Informatics and Its Applications29, 255-276.

Lent, J. and Mahmoud, H. (1996). Average-case analysis of MULTIPLE QUICKSELECT: An algorithm for finding order statistics. Statistics and Probability Letters28, 299-310.

Orlandic, R. and Mahmoud, H. (1996). O-trees, B-trees and Prefix B-trees: A comparative analysis. International Journal of Foundations of Computer Science 7, 209-226.

Fill, J., Mahmoud, H. and Szpankowski, W. (1996). On the distribution for the duration of a randomized leader election algorithm. The Annals of Applied Probability6, 1260-1283.

Lent, J. and Mahmoud, H. (1996). On tree-growing search strategies. The Annals of Applied Probability6, 1284-1302.

Mahmoud, H., Régnier, M. and Smythe, R. (1997). Analysis of Boyer-Moore-Horspoolstring-matching heuristic. Random Structures and Algorithms, Special Issue on the Analysis of Algorithms, 10, 169-187.

Mahmoud, H. (1998). On rotations in fringe-balanced binary trees. Information Processing Letters65, 41-46.

Mahmoud, H. and Smythe, R. (1998). Probabilistic Analysis of Multiple Quick Select.Algorithmica,  22, 569-584.

Mahmoud, H., Flajolet, P., Jacquet, P. and Régnier, M.  (2000). Analytic variations on bucket selection and sorting. Acta Informatica, 36, 735-760.

Kotz, S., Mahmoud, H. and Robert, P.  (2000). On generalized Pólya urn models.Statistics and Probability Letters49, 163-173.

Christophi, C. and Mahmoud, H. (2001). Distribution of the size of Random hash trees, pebbled hash trees and N-trees. Statistics and Probability Letters23, 277-288.

Tsukiji, T. and Mahmoud, H. (2001). A limit law for outputs in random circuits.Algorithmica31, 403-412.

Mahmoud, H. and Tsukiji, T. (2001). On the internal structure of random recursive circuits. Journal of Computational Applied Mathematics142, 155-171.

Hubalek, F., Hwang, H. Lew, W., Mahmoud, H., Prodinger, H. (2002). A multivariate view of random bucket digital search Trees. Journal of Algorithms44, 121-158.

Mahmoud, H. (2002). The size of random bucket trees via urn models. Acta Informatica,38, 813-838.

Mahmoud, H. and Neininger, R. (2002). Distribution of distances in random binary search trees. The Annals of Applied Probability13, 253-276.

Mahmoud, H. (2003). Urn models and connections to random trees: A review. Journal of the Iranian Statistical Society2,53-114.

Mahmoud, H. (2003). Mixed distributions in Sattolo's algorithm for cyclic permutations via randomization and derandomization. Journal of Applied Probability, 40, 790-796.

Itoh, Y. and Mahmoud, H. (2003). One-sided variations on interval trees. Journal of Applied Probability40, 654-670.

Mahmoud, H. (2003). One-sided variations binary search trees. The Annals of the Institute of Statistical Mathematics55, 885-900.

Itoh, Y., Mahmoud, H. and Takahashi, D. (2004). A stochastic model for solitons.Random Structures and Algorithms24, 51-64.

Mahmoud, H. (2004). Random sprouts a Internet models and Pólya processes. ActaInformatica41, 1-18.

Mahmoud, H. and Tsukiji, T. (2004).  Limit laws for terminal nodes in random circuits with restricted fan-out: a family of graphs generalizing binary search trees. ActaInformatica42, 1432-0525.

Javanian, M., Mahmoud, H. and Vahidi-Asl, M. (2004). Paths in m-ary interval trees.Discrete Mathematics287, 45-53.

Johnson, N., Kotz, S. and Mahmoud, H. (2004). Pólya-type urn models with multiple drawings. Journal of the Iranian Statical Society3, 165-173.

Christophi, C. and Mahmoud, H. (2005). The oscillatory distribution of distances in random tries. The Annals of Applied Probability15, 1536-1564.

Itoh, Y. and Mahmoud, H. (2005). Age statistics in the Moran population model. Statistics and Probability Letters, 74, 21-30.

Balaji, S., Mahmoud, H. and Watanabe. (2006). Distributions in the Ehrenfest process.Statistics and Probability Letters 76, 666-674.

Itoh, Y., Mahmoud, H. and Smythe, R. (2006). Probabilistic analysis of maximal gap and total accumulated length in interval division. Statistics and Probability Letters76, 1356-1363.

Balaji, S. and Mahmoud, H. (2006). Exact and Limiting distributions in diagonal Pólyaprocesses. The Annals of the Institute of Statistical Mathematics, 58, 171-185.

Aguech, R., Lasmar, N. and Mahmoud, H. (2006). Distances in random digital search trees. Acta Informatica43, 243-264.

Aguech, R., Lasmar, N. and Mahmoud, H. (2006). Limit distribution of distances in biased random tries. Journal of Applied Probability43, 1-14.

Arora, A., Jin, F., Sahin, G., Mahmoud, H. and Choi, A. (2006). Throughput analysis in wireless networks with multiple users and multiple channels. Acta Informatica43, 147-164.

Aguech, R.; Lasmar, N. and Mahmoud, H. (2007). Weighted path lengths in random binary search trees. Probability in the Engineering and Informational Sciences21, 133-141.

Cristophi, C. and Mahmoud, H. (2008). On Climbing tries. Probability in the Engineering and Informational Sciences22, 133-149.

Feng, Q., Mahmoud, H. and Panholzer, A. (2008). Phase changes in subtree varieties in random recursive trees and binary search trees. SIAM J. on Discrete Mathematics, 22, 160-184.

Feng, Q, Mahmoud, H. and Panholzer, A. (2008). Limit laws for the Randic index of random binary tree models. The Annals of the Institute of Statistical Mathematics60, 319-343.

Mahmoud, H. and Ward, M. (2008). Average-case Analysis of Cousins in m-ary Tries.Journal of Applied Probability, 45, 888-900.

Mahmoud, H. (2009). Imbalance in random digital trees. Methodology and Computing in Applied Probability11, 231-247.

Mahmoud, H. (2010). Distributional analysis of moves in Quick Select. Theoretical Computer Science411, 1763-1769.

Feng, Q. and Mahmoud, H. (2010). On the variety of shapes on the fringe of a random recursive tree. Journal of Applied Probability47, 191-200.

Mahmoud, H. (2010). The power of choice in the construction of recursive trees. Methodology and Computing in Applied Probability12, 763-773

Balaji, S. Mahmoud, H. and Zhang, T. (2010).  Phases in the diffusion of gases via theEhrenfest urn model. Journal of Applied Probability47, 841-855.

Mahmoud, H. (2010). Gaussian phases in generalized coupon collection. Advances in Applied Probability24, 1-19.

Kalpathy, R., Mahmoud, H. and Ward, M. (2011). Asymptotic properties of a leader election algorithm. Journal of Applied Probability48, 1-7.

Elmasry, A. and Mahmoud, H. (2011). Analysis of swaps in radix select. Advances in Applied Probability, 43, 524-544.

Kholfi, S. and Mahmoud, H. (2012). The class of tenable zero-balanced Pólya urns with an initially dominant color, Statistics and Probability Letters, 82, 49-57.

Mahmoud, H. and Smythe, R. (2012).  On the joint behavior of types of coupons in generalized coupon collection. Advances in Applied Probability44, 429-451.

Zhang, T. and Mahmoud H. (2012). An Urn Model for population mixing and the phases within. Methodology and Computing in Applied Probability (to appear).

Morcrette, B. and Mahmoud, H. (2012). Exactly solvable balanced tenable urns with random entries via the analytic methodology.  Discrete Mathematics and Theoretical Computer Science, proc. AQ, 219-232.

Kholfi, S. and Mahmoud, H. (2012). The class of tenable zero-balanced Pólya urn schemes: characterization and Gaussian phases. Advances in Applied Probability44, 702-728.

Mahmoud, H. and Ward, M. (2012).  The distribution of two-protected nodes in random binary search trees. Applied Mathematics Letters, 25, 2218-2222.

Mahmoud, H. (2012+). Drawing multisets of balls from tenable balanced linear urns.Probability in the Engineering and Informational Sciences (accepted).

Mahmoud, H. (2012+). The degree profile in some classes of random graphs that generalize recursive tree. Methodology and Computing in Applied Probability (tentatively accepted).

Sparks, J. and Mahmoud, H. (2012+).  Phases in the two-color tenable zero-balancedPólya process. Statistics and Probability Letters (tentatively accepted).