Richard J. Lipton

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Let G be any n-vertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2vx/-n vertices. We exhibit an algorithm which finds such a partition A, B, C in O(n) time.
We present a theoretical model for breaking various cryptographic schemes by taking advantage of random hardware faults. We show how to attack certain implementations of RSA and Rabin signatures. An implementation of RSA based on the Chinese Remainder Theorem can be broken using a single erroneous signature. Other implementations can be broken using a(More)
It is well known that every set in P has small circuits [13]. Adleman [1] has recently proved the stronger result that every set accepted in polynomial time by a randomized Turing machine has small circuits. Both these results are typical of the known relationships between uniform and nonuniform complexity bounds. They obtain a nonuniform upper bound as a(More)
We prove the existence of ε-Nash equilibrium strategies with support logarithmic in the number of pure strategies. We also show that the payoffs to all players in any (exact) Nash equilibrium can be ε-approximated by the payoffs to the players in some such logarithmic support ε-Nash equilibrium. These strategies are also uniform on a multiset(More)
It is well known that the reachability problem for directed graphs is logspace-complete for the complexity class NSPACE(log n) , and thus holds the key to the open question of whether DSPACE(logn)= NSPACE(logn) ([3,4,5,6]). Here as usual OSPACE(logn) is the class of languages that are accepted in logn space by deterministic Turing Ma chi nes, wh i 1eNSPACE((More)
We introduce the online interval scheduling problem, in which a set of intervals of the positive real line is presented to a scheduling algorithm in order of start time. Upon seeing each interval, the algorithm must decide whether or not to “schedule” it. Overlapping intervals may not be scheduled together. We give a strongly 2-competitive algorithm for the(More)