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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)

We describe a simple randomized construction for generating pairs of hash functions <i>h<inf>1</inf>,h<inf>2</inf></i> from a universe U to ranges V = [m] = (0,1,...,m-1) and W = [m] so that for every key set S ⊆ U with n = |S| ≤ m/(1 + ε) the (random) bipartite (multi)graph with node set V ∪ W and edge set… (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)

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)

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)

<i>Mutual exclusion</i> is a fundamental distributed coordination problem. Shared-memory mutual exclusion research focuses on <i>local-spin</i> algorithms and uses the <i>remote memory references</i> (RMRs) metric. A recent proof [9] established an Ω(log <i>N</i>) lower bound on the number of RMRs incurred by processes as they enter and exit the… (More)

We investigate the remote memory references (RMRs) complexity of deterministic processes that communicate by reading and writing shared memory in asynchronous cache-coherent and distributed shared-memory multiprocessors. We define a class of algorithms that we call <i>order encoding</i>. By applying information-theoretic arguments, we prove that every order… (More)

We consider asynchronous multiprocessors where processes communicate only by reading or writing shared memory. We show how to implement consensus, all comparison primitives (such as CAS and TAS), and load-linked/store-conditional using only a constant number of remote memory references (RMRs), in both the cache-coherent and the distributed-shared-memory… (More)