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 public class SortedIntArray {
 	protected int maxSize;
 	protected int [] array;
 	protected int eltCount;
 
 	public SortedIntArray(int maxelts) {
 		maxSize = maxelts;
		array = new int[maxSize];
		eltCount = 0;
	}
	
	public int getEltCount() { return eltCount; }
	public int getElt(int idx){return array[idx];}
	
	public void insert(int x) {
		array[eltCount] = x;
		eltCount++;
	}
 }


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Reading groups

  • Randomized Algorithms. Focus on classic results. Some of the papers and references below are from Motwani and Raghavan.
    • Routing. Valiant. A scheme for fast parallel communication. SIAM Journal on Computing, 11:350-361, 1982. (Should be available at AIT Library)
    • Paging. Fiat, Karp, Luby, McGeoch, Sleator, and Young. Competitive paging algorithms. Journal of Algorithms, 12:685-699, 1991. [1]
    • Byzantine agreement. Rabin. Randomized Byzantine generals. In Proceedings of the 24th Annual Symposium on Foundations of Computer Science, page 403-409, 1983. (Also, see Chor and Dwork. Randomization in Byzantine agreement. In Randomness and Computing pages 433-497. JAI Press, 1989)
    • Min-cut.
      1. David R. Karger, Clifford Stein. A New Approach to the Minimum Cut Problem. J. ACM 43(4): 601-640 (1996) [2]
      2. David R. Karger: Minimum cuts in near-linear time. J. ACM 47(1): 46-76 (2000) [3]
    • Derandomization. Nisan and Wigderson. Hardness vs. randomness. Journal of Computer and System Sciences, 49(2) pages: 149 - 167, 1994. [4]
    • Zero-knowledge.
      1. Shafi Goldwasser, Silvio Micali, and Charles Rackoff. The knowledge complexity of interactive proof-systems. In Proceedings of 17th Symposium on the Theory of Computation, Providence, Rhode Island. 1985. [5]
      2. Oded Goldreich, Silvio Micali, Avi Wigderson. Proofs that yield nothing but their validity. Journal of the ACM, volume 38, issue 3, p.690-728. July 1991. [6]
    • Isolating Lemma. Mulmuley, Vazirani, and Vazirani. Matching is as Easy as Matrix Inversion. in Proceedings of Symposium on the Theory of Computing, 1987. Combinatorica, Vol. 7, No. 1, 1987. [7]
    • Primality testing.
    • Lovasz Local Lemma.

Other possible topics:

  • Algorithmic Game Theory:
    • Probably following [8]
  • Distributed Computing: selection from [9]