TY - CONF
AB - The Massively Parallel Computation (MPC) model is an emerging model which distills core aspects of distributed and parallel computation. It has been developed as a tool to solve (typically graph) problems in systems where the input is distributed over many machines with limited space.
Recent work has focused on the regime in which machines have sublinear (in $n$, the number of nodes in the input graph) space, with randomized algorithms presented for fundamental graph problems of Maximal Matching and Maximal Independent Set. However, there have been no prior corresponding deterministic algorithms.
A major challenge underlying the sublinear space setting is that the local space of each machine might be too small to store all the edges incident to a single node. This poses a considerable obstacle compared to the classical models in which each node is assumed to know and have easy access to its incident edges. To overcome this barrier we introduce a new graph sparsification technique that deterministically computes a low-degree subgraph with additional desired properties. The degree of the nodes in this subgraph is small in the sense that the edges of each node can be now stored on a single machine. This low-degree subgraph also has the property that solving the problem on this subgraph provides \emph{significant} global progress, i.e., progress towards solving the problem for the original input graph.
Using this framework to derandomize the well-known randomized algorithm of Luby [SICOMP'86], we obtain $O(\log \Delta+\log\log n)$-round deterministic MPC algorithms for solving the fundamental problems of Maximal Matching and Maximal Independent Set with $O(n^{\epsilon})$ space on each machine for any constant $\epsilon > 0$. Based on the recent work of Ghaffari et al. [FOCS'18], this additive $O(\log\log n)$ factor is conditionally essential. These algorithms can also be shown to run in $O(\log \Delta)$ rounds in the closely related model of CONGESTED CLIQUE, improving upon the state-of-the-art bound of $O(\log^2 \Delta)$ rounds by Censor-Hillel et al. [DISC'17].
AU - Czumaj, Artur
AU - Davies, Peter
AU - Parter, Merav
ID - 7802
IS - 7
T2 - Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2020)
TI - Graph sparsification for derandomizing massively parallel computation with low space
ER -
TY - JOUR
AB - Besides pro-inflammatory roles, the ancient cytokine interleukin-17 (IL-17) modulates neural circuit function. We investigate IL-17 signaling in neurons, and the extent it can alter organismal phenotypes. We combine immunoprecipitation and mass spectrometry to biochemically characterize endogenous signaling complexes that function downstream of IL-17 receptors in C. elegans neurons. We identify the paracaspase MALT-1 as a critical output of the pathway. MALT1 mediates signaling from many immune receptors in mammals, but was not previously implicated in IL-17 signaling or nervous system function. C. elegans MALT-1 forms a complex with homologs of Act1 and IRAK and appears to function both as a scaffold and a protease. MALT-1 is expressed broadly in the C. elegans nervous system, and neuronal IL-17–MALT-1 signaling regulates multiple phenotypes, including escape behavior, associative learning, immunity and longevity. Our data suggest MALT1 has an ancient role modulating neural circuit function downstream of IL-17 to remodel physiology and behavior.
AU - Flynn, Sean M.
AU - Chen, Changchun
AU - Artan, Murat
AU - Barratt, Stephen
AU - Crisp, Alastair
AU - Nelson, Geoffrey M.
AU - Peak-Chew, Sew Yeu
AU - Begum, Farida
AU - Skehel, Mark
AU - De Bono, Mario
ID - 7804
JF - Nature Communications
TI - MALT-1 mediates IL-17 neural signaling to regulate C. elegans behavior, immunity and longevity
VL - 11
ER -
TY - CONF
AB - We consider the following decision problem EMBEDk→d in computational topology (where k ≤ d are fixed positive integers): Given a finite simplicial complex K of dimension k, does there exist a (piecewise-linear) embedding of K into ℝd?
The special case EMBED1→2 is graph planarity, which is decidable in linear time, as shown by Hopcroft and Tarjan. In higher dimensions, EMBED2→3 and EMBED3→3 are known to be decidable (as well as NP-hard), and recent results of Čadek et al. in computational homotopy theory, in combination with the classical Haefliger–Weber theorem in geometric topology, imply that EMBEDk→d can be solved in polynomial time for any fixed pair (k, d) of dimensions in the so-called metastable range .
Here, by contrast, we prove that EMBEDk→d is algorithmically undecidable for almost all pairs of dimensions outside the metastable range, namely for . This almost completely resolves the decidability vs. undecidability of EMBEDk→d in higher dimensions and establishes a sharp dichotomy between polynomial-time solvability and undecidability.
Our result complements (and in a wide range of dimensions strengthens) earlier results of Matoušek, Tancer, and the second author, who showed that EMBEDk→d is undecidable for 4 ≤ k ϵ {d – 1, d}, and NP-hard for all remaining pairs (k, d) outside the metastable range and satisfying d ≥ 4.
AU - Filakovský, Marek
AU - Wagner, Uli
AU - Zhechev, Stephan Y
ID - 7806
SN - 9781611975994
T2 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
TI - Embeddability of simplicial complexes is undecidable
VL - 2020-January
ER -
TY - CONF
AB - In a straight-line embedded triangulation of a point set P in the plane, removing an inner edge and—provided the resulting quadrilateral is convex—adding the other diagonal is called an edge flip. The (edge) flip graph has all triangulations as vertices, and a pair of triangulations is adjacent if they can be obtained from each other by an edge flip. The goal of this paper is to contribute to a better understanding of the flip graph, with an emphasis on its connectivity.
For sets in general position, it is known that every triangulation allows at least edge flips (a tight bound) which gives the minimum degree of any flip graph for n points. We show that for every point set P in general position, the flip graph is at least -vertex connected. Somewhat more strongly, we show that the vertex connectivity equals the minimum degree occurring in the flip graph, i.e. the minimum number of flippable edges in any triangulation of P, provided P is large enough. Finally, we exhibit some of the geometry of the flip graph by showing that the flip graph can be covered by 1-skeletons of polytopes of dimension (products of associahedra).
A corresponding result ((n – 3)-vertex connectedness) can be shown for the bistellar flip graph of partial triangulations, i.e. the set of all triangulations of subsets of P which contain all extreme points of P. This will be treated separately in a second part.
AU - Wagner, Uli
AU - Welzl, Emo
ID - 7807
SN - 9781611975994
T2 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
TI - Connectivity of triangulation flip graphs in the plane (Part I: Edge flips)
VL - 2020-January
ER -
TY - CONF
AB - Quantization converts neural networks into low-bit fixed-point computations which can be carried out by efficient integer-only hardware, and is standard practice for the deployment of neural networks on real-time embedded devices. However, like their real-numbered counterpart, quantized networks are not immune to malicious misclassification caused by adversarial attacks. We investigate how quantization affects a network’s robustness to adversarial attacks, which is a formal verification question. We show that neither robustness nor non-robustness are monotonic with changing the number of bits for the representation and, also, neither are preserved by quantization from a real-numbered network. For this reason, we introduce a verification method for quantized neural networks which, using SMT solving over bit-vectors, accounts for their exact, bit-precise semantics. We built a tool and analyzed the effect of quantization on a classifier for the MNIST dataset. We demonstrate that, compared to our method, existing methods for the analysis of real-numbered networks often derive false conclusions about their quantizations, both when determining robustness and when detecting attacks, and that existing methods for quantized networks often miss attacks. Furthermore, we applied our method beyond robustness, showing how the number of bits in quantization enlarges the gender bias of a predictor for students’ grades.
AU - Giacobbe, Mirco
AU - Henzinger, Thomas A
AU - Lechner, Mathias
ID - 7808
SN - 03029743
T2 - International Conference on Tools and Algorithms for the Construction and Analysis of Systems
TI - How many bits does it take to quantize your neural network?
VL - 12079
ER -