TY - CONF
AB - Consider the following random process: we are given n queues, into which elements of increasing labels are inserted uniformly at random. To remove an element, we pick two queues at random, and remove the element of lower label (higher priority) among the two. The cost of a removal is the rank of the label removed, among labels still present in any of the queues, that is, the distance from the optimal choice at each step. Variants of this strategy are prevalent in state-of-the-art concurrent priority queue implementations. Nonetheless, it is not known whether such implementations provide any rank guarantees, even in a sequential model. We answer this question, showing that this strategy provides surprisingly strong guarantees: Although the single-choice process, where we always insert and remove from a single randomly chosen queue, has degrading cost, going to infinity as we increase the number of steps, in the two choice process, the expected rank of a removed element is O(n) while the expected worst-case cost is O(n log n). These bounds are tight, and hold irrespective of the number of steps for which we run the process. The argument is based on a new technical connection between "heavily loaded" balls-into-bins processes and priority scheduling. Our analytic results inspire a new concurrent priority queue implementation, which improves upon the state of the art in terms of practical performance.
AU - Alistarh, Dan-Adrian
AU - Kopinsky, Justin
AU - Li, Jerry
AU - Nadiradze, Giorgi
ID - 791
SN - 978-145034992-5
T2 - Proceedings of the ACM Symposium on Principles of Distributed Computing
TI - The power of choice in priority scheduling
VL - Part F129314
ER -
TY - JOUR
AB - The chaotic dynamics of low-dimensional systems, such as Lorenz or Rössler flows, is guided by the infinity of periodic orbits embedded in their strange attractors. Whether this is also the case for the infinite-dimensional dynamics of Navier–Stokes equations has long been speculated, and is a topic of ongoing study. Periodic and relative periodic solutions have been shown to be involved in transitions to turbulence. Their relevance to turbulent dynamics – specifically, whether periodic orbits play the same role in high-dimensional nonlinear systems like the Navier–Stokes equations as they do in lower-dimensional systems – is the focus of the present investigation. We perform here a detailed study of pipe flow relative periodic orbits with energies and mean dissipations close to turbulent values. We outline several approaches to reduction of the translational symmetry of the system. We study pipe flow in a minimal computational cell at Re=2500, and report a library of invariant solutions found with the aid of the method of slices. Detailed study of the unstable manifolds of a sample of these solutions is consistent with the picture that relative periodic orbits are embedded in the chaotic saddle and that they guide the turbulent dynamics.
AU - Budanur, Nazmi B
AU - Short, Kimberly
AU - Farazmand, Mohammad
AU - Willis, Ashley
AU - Cvitanović, Predrag
ID - 792
JF - Journal of Fluid Mechanics
SN - 00221120
TI - Relative periodic orbits form the backbone of turbulent pipe flow
VL - 833
ER -
TY - JOUR
AB - Let P be a finite point set in the plane. A cordinary triangle in P is a subset of P consisting of three non-collinear points such that each of the three lines determined by the three points contains at most c points of P . Motivated by a question of Erdös, and answering a question of de Zeeuw, we prove that there exists a constant c > 0such that P contains a c-ordinary triangle, provided that P is not contained in the union of two lines. Furthermore, the number of c-ordinary triangles in P is Ω(| P |).
AU - Fulek, Radoslav
AU - Mojarrad, Hossein
AU - Naszódi, Márton
AU - Solymosi, József
AU - Stich, Sebastian
AU - Szedlák, May
ID - 793
JF - Computational Geometry: Theory and Applications
SN - 09257721
TI - On the existence of ordinary triangles
VL - 66
ER -
TY - JOUR
AB - We show that c-planarity is solvable in quadratic time for flat clustered graphs with three clusters if the combinatorial embedding of the underlying graph is fixed. In simpler graph-theoretical terms our result can be viewed as follows. Given a graph G with the vertex set partitioned into three parts embedded on a 2-sphere, our algorithm decides if we can augment G by adding edges without creating an edge-crossing so that in the resulting spherical graph the vertices of each part induce a connected sub-graph. We proceed by a reduction to the problem of testing the existence of a perfect matching in planar bipartite graphs. We formulate our result in a slightly more general setting of cyclic clustered graphs, i.e., the simple graph obtained by contracting each cluster, where we disregard loops and multi-edges, is a cycle.
AU - Fulek, Radoslav
ID - 794
JF - Computational Geometry: Theory and Applications
TI - C-planarity of embedded cyclic c-graphs
VL - 66
ER -
TY - JOUR
AB - We introduce a common generalization of the strong Hanani–Tutte theorem and the weak Hanani–Tutte theorem: if a graph G has a drawing D in the plane where every pair of independent edges crosses an even number of times, then G has a planar drawing preserving the rotation of each vertex whose incident edges cross each other evenly in D. The theorem is implicit in the proof of the strong Hanani–Tutte theorem by Pelsmajer, Schaefer and Štefankovič. We give a new, somewhat simpler proof.
AU - Fulek, Radoslav
AU - Kynčl, Jan
AU - Pálvölgyi, Dömötör
ID - 795
IS - 3
JF - Electronic Journal of Combinatorics
SN - 10778926
TI - Unified Hanani Tutte theorem
VL - 24
ER -
TY - JOUR
AB - We investigate transient behaviors induced by magnetic fields on the dynamics of the flow of a ferrofluid in the gap between two concentric, independently rotating cylinders. Without applying any magnetic fields, we uncover emergence of flow states constituted by a combination of a localized spiral state (SPIl) in the top and bottom of the annulus and different multi-cell flow states (SPI2v, SPI3v) with toroidally closed vortices in the interior of the bulk (SPIl+2v = SPIl + SPI2v and SPIl+3v = SPIl + SPI3v). However, when a magnetic field is presented, we observe the transient behaviors between multi-cell states passing through two critical thresholds in a strength of an axial (transverse) magnetic field. Before the first critical threshold of a magnetic field strength, multi-stable states with different number of cells could be observed. After the first critical threshold, we find the transient behavior between the three- and two-cell flow states. For more strength of magnetic field or after the second critical threshold, we discover that multi-cell states are disappeared and a localized spiral state remains to be stimulated. The studied transient behavior could be understood by the investigation of various quantities including a modal kinetic energy, a mode amplitude of the radial velocity, wavenumber, angular momentum, and torque. In addition, the emergence of new flow states and the transient behavior between their states in ferrofluidic flows indicate that richer and potentially controllable dynamics through magnetic fields could be possible in ferrofluic flow.
AU - Altmeyer, Sebastian
AU - Do, Younghae
AU - Ryu, Soorok
ID - 463
IS - 11
JF - Chaos
SN - 10541500
TI - Transient behavior between multi-cell flow states in ferrofluidic Taylor-Couette flow
VL - 27
ER -
TY - JOUR
AB - The computation of the winning set for parity objectives and for Streett objectives in graphs as well as in game graphs are central problems in computer-aided verification, with application to the verification of closed systems with strong fairness conditions, the verification of open systems, checking interface compatibility, well-formedness of specifications, and the synthesis of reactive systems. We show how to compute the winning set on n vertices for (1) parity-3 (aka one-pair Streett) objectives in game graphs in time O(n5/2) and for (2) k-pair Streett objectives in graphs in time O(n2+nklogn). For both problems this gives faster algorithms for dense graphs and represents the first improvement in asymptotic running time in 15 years.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
AU - Loitzenbauer, Veronika
ID - 464
IS - 3
JF - Logical Methods in Computer Science
SN - 18605974
TI - Improved algorithms for parity and Streett objectives
VL - 13
ER -
TY - JOUR
AB - The edit distance between two words w 1 , w 2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w 1 to w 2 . The edit distance generalizes to languages L 1 , L 2 , where the edit distance from L 1 to L 2 is the minimal number k such that for every word from L 1 there exists a word in L 2 with edit distance at most k . We study the edit distance computation problem between pushdown automata and their subclasses. The problem of computing edit distance to a pushdown automaton is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for the following problems: (1) deciding whether, for a given threshold k , the edit distance from a pushdown automaton to a finite automaton is at most k , and (2) deciding whether the edit distance from a pushdown automaton to a finite automaton is finite.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Ibsen-Jensen, Rasmus
AU - Otop, Jan
ID - 465
IS - 3
JF - Logical Methods in Computer Science
SN - 18605974
TI - Edit distance for pushdown automata
VL - 13
ER -
TY - JOUR
AB - We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives. There exist two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector. We consider optimization with respect to both objectives at once, thus unifying the existing semantics. Precisely, the goal is to optimize the expectation while ensuring the satisfaction constraint. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensure certain probabilistic guarantee). Our main results are as follows: First, we present algorithms for the decision problems which are always polynomial in the size of the MDP. We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Second, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.
AU - Chatterjee, Krishnendu
AU - Křetínská, Zuzana
AU - Kretinsky, Jan
ID - 466
IS - 2
JF - Logical Methods in Computer Science
SN - 18605974
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
VL - 13
ER -
TY - JOUR
AB - Recently there has been a significant effort to handle quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, some basic system properties such as average response time cannot be expressed using weighted automata or in any other known decidable formalism. In this work, we introduce nested weighted automata as a natural extension of weighted automata, which makes it possible to express important quantitative properties such as average response time. In nested weighted automata, a master automaton spins off and collects results from weighted slave automata, each of which computes a quantity along a finite portion of an infinite word. Nested weighted automata can be viewed as the quantitative analogue of monitor automata, which are used in runtime verification. We establish an almost-complete decidability picture for the basic decision problems about nested weighted automata and illustrate their applicability in several domains. In particular, nested weighted automata can be used to decide average response time properties.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 467
IS - 4
JF - ACM Transactions on Computational Logic (TOCL)
SN - 15293785
TI - Nested weighted automata
VL - 18
ER -