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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)

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)

- Martin Aumüller, Martin Dietzfelbinger, Philipp Woelfel
- Algorithmica
- 2012

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)

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)

Long-lived renaming allows processes to repeatedly get distinct names from a small name space and release these names. This paper presents two long-lived renaming algorithms in which the name a process gets is bounded above by the number of processes currently occupying a name or performing one of these operations. The first is asynchronous, uses LL/SC… (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)

Linearizability is the gold standard among algorithm designers for deducing the correctness of a distributed algorithm using implemented shared objects from the correctness of the corresponding algorithm using atomic versions of the same objects. We show that linearizability does not suffice for this purpose when processes can exploit randomization, and we… (More)

We study the time and space complexity of randomized Test-And-Set (TAS) implementations from atomic read/write registers in asynchronous shared memory models with <i>n</i> processes. We present an adaptive TAS algorithm with an expected (individual) step complexity of <i>O</i>(log<sup>*</sup> <i>k</i>), for contention <i>k</i>, against the oblivious… (More)