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.

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.