Optimal Orthogonal Graph Drawing with Convex Bend Costs

Traditionally, the quality of orthogonal planar drawings is quantified by either the total number of bends, or the maximum number of bends per edge. However, this neglects that in typical applications, edges have varying importance. Moreover, as bend minimization over all planar embeddings is NP-hard, most approaches focus on a fixed planar embedding. We consider the problem OptimalFlexDraw that is defined as follows. Given a planar graph G on n vertices with maximum degree 4 and for each edge e a cost function cost_e : N_0 --> R defining costs depending on the number of bends on e, compute an orthogonal drawing of G of minimum cost. Note that this optimizes over all planar embeddings of the input graphs, and the cost functions allow fine-grained control on the bends of edges. In this generality OptimalFlexDraw is NP-hard. We show that it can be solved efficiently if 1) the cost function of each edge is convex and 2) the first bend on each edge does not cause any cost (which is a condition similar to the positive flexibility for the decision problem FlexDraw). Moreover, we show the existence of an optimal solution with at most three bends per edge except for a single edge per block (maximal biconnected component) with up to four bends. For biconnected graphs we obtain a running time of O(n T_flow(n)), where T_flow(n) denotes the time necessary to compute a minimum-cost flow in a planar flow network with multiple sources and sinks. For connected graphs that are not biconnected we need an additional factor of O(n).Comment: 31 pages, 14 figure

The Stochastic Firefighter Problem

The dynamics of infectious diseases spread is crucial in determining their risk and offering ways to contain them. We study sequential vaccination of individuals in networks. In the original (deterministic) version of the Firefighter problem, a fire breaks out at some node of a given graph. At each time step, b nodes can be protected by a firefighter and then the fire spreads to all unprotected neighbors of the nodes on fire. The process ends when the fire can no longer spread. We extend the Firefighter problem to a probabilistic setting, where the infection is stochastic. We devise a simple policy that only vaccinates neighbors of infected nodes and is optimal on regular trees and on general graphs for a sufficiently large budget. We derive methods for calculating upper and lower bounds of the expected number of infected individuals, as well as provide estimates on the budget needed for containment in expectation. We calculate these explicitly on trees, d-dimensional grids, and Erd\H{o}s R\'{e}nyi graphs. Finally, we construct a state-dependent budget allocation strategy and demonstrate its superiority over constant budget allocation on real networks following a first order acquaintance vaccination policy

Link Failure Recovery over Very Large Arbitrary Networks: The Case of Coding

Network coding-based link failure recovery techniques provide near-hitless recovery and offer high capacity efficiency. Diversity coding is the first technique to incorporate coding in this field and is easy to implement over small arbitrary networks. However, its capacity efficiency is restricted by its systematic coding and high design complexity even though its design complexity is lower than the other coding-based recovery techniques. Alternative techniques mitigate some of these limitations, but they are difficult to implement over arbitrary networks. In this paper, we propose a simple column generation-based design algorithm and a novel advanced diversity coding technique to achieve near-hitless recovery over arbitrary networks. The design framework consists of two parts: a main problem and subproblem. Main problem is realized with Linear Programming (LP) and Integer Linear Programming (ILP), whereas the subproblem can be realized with different methods. The simulation results suggest that both the novel coding structure and the novel design algorithm lead to higher capacity efficiency for near-hitless recovery. The novel design algorithm simplifies the capacity placement problem which enables implementing diversity coding-based techniques on very large arbitrary networks.Comment: To be submitted to IEEE Transactions on Communication

A Distributed Clustering Algorithm for Dynamic Networks

We propose an algorithm that builds and maintains clusters over a network subject to mobility. This algorithm is fully decentralized and makes all the different clusters grow concurrently. The algorithm uses circulating tokens that collect data and move according to a random walk traversal scheme. Their task consists in (i) creating a cluster with the nodes it discovers and (ii) managing the cluster expansion; all decisions affecting the cluster are taken only by a node that owns the token. The size of each cluster is maintained higher than $m$ nodes ($m$ is a parameter of the algorithm). The obtained clustering is locally optimal in the sense that, with only a local view of each clusters, it computes the largest possible number of clusters (\emph{ie} the sizes of the clusters are as close to $m$ as possible). This algorithm is designed as a decentralized control algorithm for large scale networks and is mobility-adaptive: after a series of topological changes, the algorithm converges to a clustering. This recomputation only affects nodes in clusters in which topological changes happened, and in adjacent clusters

Sub-families of Baxter Permutations Based on Pattern Avoidance

Baxter permutations are a class of permutations which are in bijection with a class of floorplans that arise in chip design called mosaic floorplans. We study a subclass of mosaic floorplans called $HFO_k$ defined from mosaic floorplans by placing certain geometric restrictions. This naturally leads to studying a subclass of Baxter permutations. This subclass of Baxter permutations are characterized by pattern avoidance. We establish a bijection, between the subclass of floorplans we study and a subclass of Baxter permutations, based on the analogy between decomposition of a floorplan into smaller blocks and block decomposition of permutations. Apart from the characterization, we also answer combinatorial questions on these classes. We give an algebraic generating function (but without a closed form solution) for the number of permutations, an exponential lower bound on growth rate, and a linear time algorithm for deciding membership in each subclass. Based on the recurrence relation describing the class, we also give a polynomial time algorithm for enumeration. We finally prove that Baxter permutations are closed under inverse based on an argument inspired from the geometry of the corresponding mosaic floorplans. This proof also establishes that the subclass of Baxter permutations we study are also closed under inverse. Characterizing permutations instead of the corresponding floorplans can be helpful in reasoning about the solution space and in designing efficient algorithms for floorplanning

A Uniform Self-Stabilizing Minimum Diameter Spanning Tree Algorithm

We present a uniform self-stabilizing algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of an arbitrary positively real-weighted graph. Our algorithm consists in two stages of stabilizing protocols. The first stage is a uniform randomized stabilizing {\em unique naming} protocol, and the second stage is a stabilizing {\em MDST} protocol, designed as a {\em fair composition} of Merlin--Segall's stabilizing protocol and a distributed deterministic stabilizing protocol solving the (MDST) problem. The resulting randomized distributed algorithm presented herein is a composition of the two stages; it stabilizes in $O(n\Delta+{\cal D}^2 + n \log\log n)$ expected time, and uses $O(n^2\log n + n \log W)$ memory bits (where $n$ is the order of the graph, $\Delta$ is the maximum degree of the network, $\cal D$ is the diameter in terms of hops, and $W$ is the largest edge weight). To our knowledge, our protocol is the very first distributed algorithm for the (MDST) problem. Moreover, it is fault-tolerant and works for any anonymous arbitrary network.Comment: 14 pages; International conf\'erence; Uniform self-stabilizing variant of the problem, 9th International Workshop on Distributed Algorithms (WDAG'95), Mont-Saint-Michel : France (1995

Calibration of Phone Likelihoods in Automatic Speech Recognition

In this paper we study the probabilistic properties of the posteriors in a speech recognition system that uses a deep neural network (DNN) for acoustic modeling. We do this by reducing Kaldi's DNN shared pdf-id posteriors to phone likelihoods, and using test set forced alignments to evaluate these using a calibration sensitive metric. Individual frame posteriors are in principle well-calibrated, because the DNN is trained using cross entropy as the objective function, which is a proper scoring rule. When entire phones are assessed, we observe that it is best to average the log likelihoods over the duration of the phone. Further scaling of the average log likelihoods by the logarithm of the duration slightly improves the calibration, and this improvement is retained when tested on independent test data.Comment: Rejected by Interspeech 2016. I would love to include the reviews, but there is no space for that here (400 characters

A Universal Grammar-Based Code For Lossless Compression of Binary Trees

We consider the problem of lossless compression of binary trees, with the aim of reducing the number of code bits needed to store or transmit such trees. A lossless grammar-based code is presented which encodes each binary tree into a binary codeword in two steps. In the first step, the tree is transformed into a context-free grammar from which the tree can be reconstructed. In the second step, the context-free grammar is encoded into a binary codeword. The decoder of the grammar-based code decodes the original tree from its codeword by reversing the two encoding steps. It is shown that the resulting grammar-based binary tree compression code is a universal code on a family of probabilistic binary tree source models satisfying certain weak restrictions

Self-Stabilizing Wavelets and r-Hops Coordination

We introduce a simple tool called the wavelet (or, r-wavelet) scheme. Wavelets deals with coordination among processes which are at most r hops away of each other. We present a selfstabilizing solution for this scheme. Our solution requires no underlying structure and works in arbritrary anonymous networks, i.e., no process identifier is required. Moreover, our solution works under any (even unfair) daemon. Next, we use the wavelet scheme to design self-stabilizing layer clocks. We show that they provide an efficient device in the design of local coordination problems at distance r, i.e., r-barrier synchronization and r-local resource allocation (LRA) such as r-local mutual exclusion (LME), r-group mutual exclusion (GME), and r-Reader/Writers. Some solutions to the r-LRA problem (e.g., r-LME) also provide transformers to transform algorithms written assuming any r-central daemon into algorithms working with any distributed daemon

FPGA-based Accelerators of Deep Learning Networks for Learning and Classification: A Review

Due to recent advances in digital technologies, and availability of credible data, an area of artificial intelligence, deep learning, has emerged, and has demonstrated its ability and effectiveness in solving complex learning problems not possible before. In particular, convolution neural networks (CNNs) have demonstrated their effectiveness in image detection and recognition applications. However, they require intensive CPU operations and memory bandwidth that make general CPUs fail to achieve desired performance levels. Consequently, hardware accelerators that use application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), and graphic processing units (GPUs) have been employed to improve the throughput of CNNs. More precisely, FPGAs have been recently adopted for accelerating the implementation of deep learning networks due to their ability to maximize parallelism as well as due to their energy efficiency. In this paper, we review recent existing techniques for accelerating deep learning networks on FPGAs. We highlight the key features employed by the various techniques for improving the acceleration performance. In addition, we provide recommendations for enhancing the utilization of FPGAs for CNNs acceleration. The techniques investigated in this paper represent the recent trends in FPGA-based accelerators of deep learning networks. Thus, this review is expected to direct the future advances on efficient hardware accelerators and to be useful for deep learning researchers.Comment: This article has been accepted for publication in IEEE Access (December, 2018