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We present a symbolic OBDD algorithm for topological sorting which requires O(log 2 N) OBDD operations. Then we analyze its true runtime for the directed grid graph and show an upper bound of O(log 4 N). This is the first true runtime analysis of a symbolic OBDD algorithm for a fundamental graph problem, and it demonstrates that one can hope that the(More)
Bryant [5] has shown that any OBDD for the function MUL n−1,n , i.e. the middle bit of the n-bit multiplication, requires at least 2 n/8 nodes. In this paper a stronger lower bound of essentially 2 n/2 /61 is proven by a new technique, using a universal family of hash functions. As a consequence, one cannot hope anymore to verify e.g. 128-bit multiplication(More)
Branching programs (BPs) are a well-established computation and representation model for Boolean functions. Especially read-once branching programs (BP1s) have been studied intensively. Exponential lower bounds on the BP1 complexity of explicit functions have been known for a long time. Nevertheless, the proof of exponential lower bounds on the read-once(More)
We prove exponential size lower bounds for nondeterministic and randomized read-<i>k</i> BPs as well as a time-space tradeoff lower bound for unrestricted, deterministic multi-way BPs computing the middle bit of integer multiplication. The lower bound for randomized read-<i>k</i> BPs is superpolynomial as long as the error probability is superpolynomially(More)
We solve some fundamental problems in the number-on-forehead (NOF) k-party communication model. We show that there exists a function which has at most logarithmic communication complexity for randomized protocols with a one-sided error probability of 1/3 but which has linear communication complexity for deterministic protocols. The result is true for k = n(More)
It is shown that for cuckoo hashing with a stash as proposed by Kirsch et al. (Proc. 16th European Symposium on Algorithms (ESA), pp. 611–622, Springer, Berlin, 2008) families of very simple hash functions can be used, maintaining the favorable performance guarantees: with constant stash size s the probability of a rehash is O(1/n s+1), the lookup time and(More)
In this paper, the space requirements for the OBDD representation of certain graph classes, specifically cographs, several types of graphs with few P4s, unit interval graphs, interval graphs and bipartite graphs are investigated. Upper and lower bounds are proven for all these graph classes and it is shown that in most (but not all) cases a representation(More)