Concurrent Disjoint Set Union

We develop and analyze concurrent algorithms for the disjoint set union (union-find) problem in the shared memory, asynchronous multiprocessor model of computation, with CAS (compare and swap) or DCAS (double compare and swap) as the synchronization primitive. We give a deterministic bounded wait-free algorithm that uses DCAS and has a total work bound of $O(m \cdot (\log(np/m + 1) + \alpha(n, m/(np)))$ for a problem with $n$ elements and $m$ operations solved by $p$ processes, where $\alpha$ is a functional inverse of Ackermann's function. We give two randomized algorithms that use only CAS and have the same work bound in expectation. The analysis of the second randomized algorithm is valid even if the scheduler is adversarial. Our DCAS and randomized algorithms take $O(\log n)$ steps per operation, worst-case for the DCAS algorithm, high-probability for the randomized algorithms. Our work and step bounds grow only logarithmically with $p$, making our algorithms truly scalable. We prove that for a class of symmetric algorithms that includes ours, no better step or work bound is possible.Comment: 40 pages, combines ideas in two previous PODC paper

Minimum Cost Flows in Graphs with Unit Capacities

We consider the minimum cost flow problem on graphs with unit capacities and its special cases. In previous studies, special purpose algorithms exploiting the fact that capacities are one have been developed. In contrast, for maximum flow with unit capacities, the best bounds are proven for slight modifications of classical blocking flow and push-relabel algorithms. In this paper we show that the classical cost scaling algorithms of Goldberg and Tarjan (for general integer capacities) applied to a problem with unit capacities achieve or improve the best known bounds. For weighted bipartite matching we establish a bound of O(sqrt{rm}log C) on a slight variation of this algorithm. Here r is the size of the smaller side of the bipartite graph, m is the number of edges, and C is the largest absolute value of an arc-cost. This simplifies a result of [Duan et al. 2011] and improves the bound, answering an open question of [Tarjan and Ramshaw 2012]. For graphs with unit vertex capacities we establish a novel O(sqrt{n}mlog(nC)) bound. We also give the first cycle canceling algorithm for minimum cost flow with unit capacities. The algorithm naturally generalizes the single source shortest path algorithm of [Goldberg 1995]

Interaction of quasilocal harmonic modes and boson peak in glasses

The direct proportionality relation between the boson peak maximum in glasses, $\omega_b$, and the Ioffe-Regel crossover frequency for phonons, $\omega_d$, is established. For several investigated materials $\omega_b = (1.5\pm 0.1)\omega_d$. At the frequency $\omega_d$ the mean free path of the phonons $l$ becomes equal to their wavelength because of strong resonant scattering on quasilocal harmonic oscillators. Above this frequency phonons cease to exist. We prove that the established correlation between $\omega_b$ and $\omega_d$ holds in the general case and is a direct consequence of bilinear coupling of quasilocal oscillators with the strain field.Comment: RevTex, 4 pages, 1 figur

On the Number of Synchronizing Colorings of Digraphs

We deal with $k$-out-regular directed multigraphs with loops (called simply \emph{digraphs}). The edges of such a digraph can be colored by elements of some fixed $k$-element set in such a way that outgoing edges of every vertex have different colors. Such a coloring corresponds naturally to an automaton. The road coloring theorem states that every primitive digraph has a synchronizing coloring. In the present paper we study how many synchronizing colorings can exist for a digraph with $n$ vertices. We performed an extensive experimental investigation of digraphs with small number of vertices. This was done by using our dedicated algorithm exhaustively enumerating all small digraphs. We also present a series of digraphs whose fraction of synchronizing colorings is equal to $1-1/k^d$, for every $d \ge 1$ and the number of vertices large enough. On the basis of our results we state several conjectures and open problems. In particular, we conjecture that $1-1/k$ is the smallest possible fraction of synchronizing colorings, except for a single exceptional example on 6 vertices for $k=2$.Comment: CIAA 2015. The final publication is available at http://link.springer.com/chapter/10.1007/978-3-319-22360-5_1

A quasi-linear algorithm to compute the tree of shapes of n-D images

International audienceTo compute the morphological self-dual representation of images, namely the tree of shapes, the state-of-the-art algorithms do not have a satisfactory time complexity. Furthermore the proposed algorithms are only effective for 2D images and they are far from being simple to implement. That is really penalizing since a self-dual representation of images is a structure that gives rise to many powerful operators and applications, and that could be very useful for 3D images. In this paper we propose a simple-to-write algorithm to compute the tree of shapes; it works for \nD images and has a quasi-linear complexity when data quantization is low, typically 12~bits or less. To get that result, this paper introduces a novel representation of images that has some amazing properties of continuity, while remaining discrete

Inference of Well-Typings for Logic Programs with Application to Termination Analysis

This paper develops a method to infer a polymorphic well-typing for a logic program. One of the main motivations is to contribute to a better automation of termination analysis in logic programs, by deriving types from which norms can automatically be constructed. Previous work on type-based termination analysis used either types declared by the user, or automatically generated monomorphic types describing the success set of predicates. Declared types are typically more precise and result in stronger termination conditions than those obtained with inferred types. Our type inference procedure involves solving set constraints generated from the program and derives a well-typing in contrast to a success-set approximation. Experiments show that our automatically inferred well-typings are close to the declared types and thus result in termination conditions that are as good as those obtained with declared types for all our experiments to date. We describe the method, its implementation and experiments with termination analysis based on the inferred types

Overcoming controllability problems in distributed testing from an input output transition system

This is the Pre-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 Springer VerlagThis paper concerns the testing of a system with physically distributed interfaces, called ports, at which it interacts with its environment. We place a tester at each port and the tester at port p observes events at p only. This can lead to controllability problems, where the observations made by the tester at a port p are not sufficient for it to be able to know when to send an input. It is known that there are test objectives, such as executing a particular transition, that cannot be achieved if we restrict attention to test cases that have no controllability problems. This has led to interest in schemes where the testers at the individual ports send coordination messages to one another through an external communications network in order to overcome controllability problems. However, such approaches have largely been studied in the context of testing from a deterministic finite state machine. This paper investigates the use of coordination messages to overcome controllability problems when testing from an input output transition system and gives an algorithm for introducing sufficient messages. It also proves that the problem of minimising the number of coordination messages used is NP-hard

Computing the vertices of tropical polyhedra using directed hypergraphs

We establish a characterization of the vertices of a tropical polyhedron defined as the intersection of finitely many half-spaces. We show that a point is a vertex if, and only if, a directed hypergraph, constructed from the subdifferentials of the active constraints at this point, admits a unique strongly connected component that is maximal with respect to the reachability relation (all the other strongly connected components have access to it). This property can be checked in almost linear-time. This allows us to develop a tropical analogue of the classical double description method, which computes a minimal internal representation (in terms of vertices) of a polyhedron defined externally (by half-spaces or hyperplanes). We provide theoretical worst case complexity bounds and report extensive experimental tests performed using the library TPLib, showing that this method outperforms the other existing approaches.Comment: 29 pages (A4), 10 figures, 1 table; v2: Improved algorithm in section 5 (using directed hypergraphs), detailed appendix; v3: major revision of the article (adding tropical hyperplanes, alternative method by arrangements, etc); v4: minor revisio

Specific-Heat Exponent of Random-Field Systems via Ground-State Calculations

Exact ground states of three-dimensional random field Ising magnets (RFIM) with Gaussian distribution of the disorder are calculated using graph-theoretical algorithms. Systems for different strengths h of the random fields and sizes up to N=96^3 are considered. By numerically differentiating the bond-energy with respect to h a specific-heat like quantity is obtained, which does not appear to diverge at the critical point but rather exhibits a cusp. We also consider the effect of a small uniform magnetic field, which allows us to calculate the T=0 susceptibility. From a finite-size scaling analysis, we obtain the critical exponents \nu=1.32(7), \alpha=-0.63(7), \eta=0.50(3) and find that the critical strength of the random field is h_c=2.28(1). We discuss the significance of the result that \alpha appears to be strongly negative.Comment: 9 pages, 9 figures, 1 table, revtex revised version, slightly extende

Formal Quantitative Analysis of Reaction Networks Using Chemical Organisation Theory

Proceedings of CMSB 2016 will be published as a volume in Springer's Lecture Notes in Computer Science / Lecture Notes in Bioinformatics series (LNCS/LNBI)