A provably tight delay-driven concurrently congestion mitigating global routing algorithm

Routing is a very important step in VLSI physical design. A set of nets are routed under delay and resource constraints in multi-net global routing. In this paper a delay-driven congestion-aware global routing algorithm is developed, which is a heuristic based method to solve a multi-objective NP-hard optimization problem. The proposed delay-driven Steiner tree construction method is of O(n(2) log n) complexity, where n is the number of terminal points and it provides n-approximation solution of the critical time minimization problem for a certain class of grid graphs. The existing timing-driven method (Hu and Sapatnekar, 2002) has a complexity O(n(4)) and is implemented on nets with small number of sinks. Next we propose a FPTAS Gradient algorithm for minimizing the total overflow. This is a concurrent approach considering all the nets simultaneously contrary to the existing approaches of sequential rip-up and reroute. The algorithms are implemented on ISPD98 derived benchmarks and the drastic reduction of overflow is observed. (C) 2014 Elsevier Inc. All rights reserved.

Hydrodynamics from scalar black branes

In this paper, using the Gauge/gravity duality techniques, we explore the hydrodynamic regime of a very special class of strongly coupled QFTs that come up with an emerging UV length scale in the presence of a negative hyperscaling violating exponent. The dual gravitational counterpart for these QFTs consists of scalar dressed black brane solutions of exactly integrable Einstein-scalar gravity model with Domain Wall (DW) asymptotics. In the first part of our analysis we compute the R-charge diffusion for the boundary theory and find that (unlike the case for the pure AdS (4) black branes) it scales quite non trivially with the temperature. In the second part of our analysis, we compute the eta/s ratio both in the non extremal as well as in the extremal limit of these special class of gauge theories and it turns out to be equal to 1/4 pi in both the cases. These results therefore suggest that the quantum critical systems in the presence of (negative) hyperscaling violation at UV, might fall under a separate universality class as compared to those conventional quantum critical systems with the usual AdS (4) duals.

Holographic charge diffusion in non-relativistic branes

In this paper, based on the principles of gauge/gravity duality and considering the so called hydrodynamic limit we compute various charge transport properties for a class of strongly coupled non-relativistic CFTs corresponding to z=2 fixed point whose dual gravitational counter part could be realized as the consistent truncation of certain non-relativistic Dp branes in the non-extremal limit. From our analysis we note that unlike the case for the AdS black branes, the charge diffusion constant in the non-relativistic background scales differently with the temperature. This shows a possible violation of the universal bound on the charge conductivity to susceptibility ratio in the context of non-relativistic holography. (C) 2015 The Author. Published by Elsevier B.V.

PERCOLATION ON THE INFORMATION-THEORETICALLY SECURE SIGNAL TO INTERFERENCE RATIO GRAPH

We consider a continuum percolation model consisting of two types of nodes, namely legitimate and eavesdropper nodes, distributed according to independent Poisson point processes in R-2 of intensities lambda and lambda(E), respectively. A directed edge from one legitimate node A to another legitimate node B exists provided that the strength of the signal transmitted from node A that is received at node B is higher than that received at any eavesdropper node. The strength of the signal received at a node from a legitimate node depends not only on the distance between these nodes, but also on the location of the other legitimate nodes and an interference suppression parameter gamma. The graph is said to percolate when there exists an infinitely connected component. We show that for any finite intensity lambda(E) of eavesdropper nodes, there exists a critical intensity lambda(c) < infinity such that for all lambda > lambda(c) the graph percolates for sufficiently small values of the interference parameter. Furthermore, for the subcritical regime, we show that there exists a lambda(0) such that for all lambda < lambda(0) <= lambda(c) a suitable graph defined over eavesdropper node connections percolates that precludes percolation in the graphs formed by the legitimate nodes.

On the Parameterized Complexity of Finding Separators with Non-Hereditary Properties

We study the problem of finding small s-t separators that induce graphs having certain properties. It is known that finding a minimum clique s-t separator is polynomial-time solvable (Tarjan in Discrete Math. 55:221-232, 1985), while for example the problems of finding a minimum s-t separator that induces a connected graph or forms an independent set are fixed-parameter tractable when parameterized by the size of the separator (Marx et al. in ACM Trans. Algorithms 9(4): 30, 2013). Motivated by these results, we study properties that generalize cliques, independent sets, and connected graphs, and determine the complexity of finding separators satisfying these properties. We investigate these problems also on bounded-degree graphs. Our results are as follows: Finding a minimum c-connected s-t separator is FPT for c=2 and W1]-hard for any ca parts per thousand yen3. Finding a minimum s-t separator with diameter at most d is W1]-hard for any da parts per thousand yen2. Finding a minimum r-regular s-t separator is W1]-hard for any ra parts per thousand yen1. For any decidable graph property, finding a minimum s-t separator with this property is FPT parameterized jointly by the size of the separator and the maximum degree. Finding a connected s-t separator of minimum size does not have a polynomial kernel, even when restricted to graphs of maximum degree at most 3, unless .

A Statistical Model of Current Loops and Magnetic Monopoles

We formulate a natural model of loops and isolated vertices for arbitrary planar graphs, which we call the monopole-dimer model. We show that the partition function of this model can be expressed as a determinant. We then extend the method of Kasteleyn and Temperley-Fisher to calculate the partition function exactly in the case of rectangular grids. This partition function turns out to be a square of a polynomial with positive integer coefficients when the grid lengths are even. Finally, we analyse this formula in the infinite volume limit and show that the local monopole density, free energy and entropy can be expressed in terms of well-known elliptic functions. Our technique is a novel determinantal formula for the partition function of a model of isolated vertices and loops for arbitrary graphs.

Non-Abelian gauge redundancy and entropic ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. Therefore one reaches the remarkable possibility that there may be many entropies for a given state. We show that this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This ambiguity in entropy, which can occur at zero temperature, can often be traced to a gauge symmetry emergent from the non-trivial topological character of the configuration space of the underlying system. We also establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix. After demonstrating this entropy ambiguity for the simple example of the algebra of 2 x 2 matrices, we argue that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. We work out the simplest situation with such non-Abelian symmetry, that of an ethylene molecule.

Quantum fluctuations and thermal dissipation in higher derivative gravity

In this paper, based on the AdS(2)/CFT1 prescription, we explore the low frequency behavior of quantum two point functions for a special class of strongly coupled CFTs in one dimension whose dual gravitational counterpart consists of extremal black hole solutions in higher derivative theories of gravity defined over an asymptotically AdS spacetime. The quantum critical points thus described are supposed to correspond to a very large value of the dynamic exponent (z -> infinity). In our analysis, we find that quantum fluctuations are enhanced due to the higher derivative corrections in the bulk which in turn increases the possibility of quantum phase transition near the critical point. On the field theory side, such higher derivative effects would stand for the corrections appearing due to the finite coupling in the gauge theory. Finally, we compute the coefficient of thermal diffusion at finite coupling corresponding to Gauss Bonnet corrected charged Lifshitz black holes in the bulk. We observe an important crossover corresponding to z = 5 fixed point. (C) 2015 The Author. Published by Elsevier B.V.

Taming Control Divergence in GPUs through Control Flow Linearization

Branch divergence is a very commonly occurring performance problem in GPGPU in which the execution of diverging branches is serialized to execute only one control flow path at a time. Existing hardware mechanism to reconverge threads using a stack causes duplicate execution of code for unstructured control flow graphs. Also the stack mechanism cannot effectively utilize the available parallelism among diverging branches. Further, the amount of nested divergence allowed is also limited by depth of the branch divergence stack. In this paper we propose a simple and elegant transformation to handle all of the above mentioned problems. The transformation converts an unstructured CFG to a structured CFG without duplicating user code. It incurs only a linear increase in the number of basic blocks and also the number of instructions. Our solution linearizes the CFG using a predicate variable. This mechanism reconverges the divergent threads as early as possible. It also reduces the depth of the reconvergence stack. The available parallelism in nested branches can be effectively extracted by scheduling the basic blocks to reduce the effect of stalls due to memory accesses. It can also increase execution efficiency of nested loops with different trip counts for different threads. We implemented the proposed transformation at PTX level using the Ocelot compiler infrastructure. We evaluated the technique using various benchmarks to show that it can be effective in handling the performance problem due to divergence in unstructured CFGs.

Query Click and Text Similarity Graph for Query Suggestions

Query suggestion is an important feature of the search engine with the explosive and diverse growth of web contents. Different kind of suggestions like query, image, movies, music and book etc. are used every day. Various types of data sources are used for the suggestions. If we model the data into various kinds of graphs then we can build a general method for any suggestions. In this paper, we have proposed a general method for query suggestion by combining two graphs: (1) query click graph which captures the relationship between queries frequently clicked on common URLs and (2) query text similarity graph which finds the similarity between two queries using Jaccard similarity. The proposed method provides literally as well as semantically relevant queries for users' need. Simulation results show that the proposed algorithm outperforms heat diffusion method by providing more number of relevant queries. It can be used for recommendation tasks like query, image, and product suggestion.

Falcon: A Graph Manipulation Language for Heterogeneous Systems

Graph algorithms have been shown to possess enough parallelism to keep several computing resources busy-even hundreds of cores on a GPU. Unfortunately, tuning their implementation for efficient execution on a particular hardware configuration of heterogeneous systems consisting of multicore CPUs and GPUs is challenging, time consuming, and error prone. To address these issues, we propose a domain-specific language (DSL), Falcon, for implementing graph algorithms that (i) abstracts the hardware, (ii) provides constructs to write explicitly parallel programs at a higher level, and (iii) can work with general algorithms that may change the graph structure (morph algorithms). We illustrate the usage of our DSL to implement local computation algorithms (that do not change the graph structure) and morph algorithms such as Delaunay mesh refinement, survey propagation, and dynamic SSSP on GPU and multicore CPUs. Using a set of benchmark graphs, we illustrate that the generated code performs close to the state-of-the-art hand-tuned implementations.