Rainbow Connection Number of Graph Power and Graph Products

Rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges so that every pair of vertices is connected by at least one path in which no two edges are colored the same (note that the coloring need not be proper). In this paper we study the rainbow connection number with respect to three important graph product operations (namely the Cartesian product, the lexicographic product and the strong product) and the operation of taking the power of a graph. In this direction, we show that if G is a graph obtained by applying any of the operations mentioned above on non-trivial graphs, then rc(G) a parts per thousand currency sign 2r(G) + c, where r(G) denotes the radius of G and . In general the rainbow connection number of a bridgeless graph can be as high as the square of its radius 1]. This is an attempt to identify some graph classes which have rainbow connection number very close to the obvious lower bound of diameter (and thus the radius). The bounds reported are tight up to additive constants. The proofs are constructive and hence yield polynomial time -factor approximation algorithms.

Solving Dynamic Constraint Single Objective Functions using a Nature Inspired Technique

We present in this paper a new algorithm based on Particle Swarm Optimization (PSO) for solving Dynamic Single Objective Constrained Optimization (DCOP) problems. We have modified several different parameters of the original particle swarm optimization algorithm by introducing new types of particles for local search and to detect changes in the search space. The algorithm is tested with a known benchmark set and compare with the results with other contemporary works. We demonstrate the convergence properties by using convergence graphs and also the illustrate the changes in the current benchmark problems for more realistic correspondence to practical real world problems.

Compiler/Runtime Framework for Dynamic Dataflow Parallelization of Tiled Programs

Task-parallel languages are increasingly popular. Many of them provide expressive mechanisms for intertask synchronization. For example, OpenMP 4.0 will integrate data-driven execution semantics derived from the StarSs research language. Compared to the more restrictive data-parallel and fork-join concurrency models, the advanced features being introduced into task-parallelmodels in turn enable improved scalability through load balancing, memory latency hiding, mitigation of the pressure on memory bandwidth, and, as a side effect, reduced power consumption. In this article, we develop a systematic approach to compile loop nests into concurrent, dynamically constructed graphs of dependent tasks. We propose a simple and effective heuristic that selects the most profitable parallelization idiom for every dependence type and communication pattern. This heuristic enables the extraction of interband parallelism (cross-barrier parallelism) in a number of numerical computations that range from linear algebra to structured grids and image processing. The proposed static analysis and code generation alleviates the burden of a full-blown dependence resolver to track the readiness of tasks at runtime. We evaluate our approach and algorithms in the PPCG compiler, targeting OpenStream, a representative dataflow task-parallel language with explicit intertask dependences and a lightweight runtime. Experimental results demonstrate the effectiveness of the approach.

LOWER BOUNDS FOR BOXICITY

An axis-parallel b-dimensional box is a Cartesian product R-1 x R-2 x ... x R-b where R-i is a closed interval of the form a(i),b(i)] on the real line. For a graph G, its boxicity box(G) is the minimum dimension b, such that G is representable as the intersection graph of boxes in b-dimensional space. Although boxicity was introduced in 1969 and studied extensively, there are no significant results on lower bounds for boxicity. In this paper, we develop two general methods for deriving lower bounds. Applying these methods we give several results, some of which are listed below: 1. The boxicity of a graph on n vertices with no universal vertices and minimum degree delta is at least n/2(n-delta-1). 2. Consider the g(n,p) model of random graphs. Let p <= 1 - 40logn/n(2.) Then with high `` probability, box(G) = Omega(np(1 - p)). On setting p = 1/2 we immediately infer that almost all graphs have boxicity Omega(n). Another consequence of this result is as follows: For any positive constant c < 1, almost all graphs on n vertices and m <= c((n)(2)) edges have boxicity Omega(m/n). 3. Let G be a connected k-regular graph on n vertices. Let lambda be the second largest eigenvalue in absolute value of the adjacency matrix of G. Then, the boxicity of G is a least (kappa(2)/lambda(2)/log(1+kappa(2)/lambda(2))) (n-kappa-1/2n). 4. For any positive constant c 1, almost all balanced bipartite graphs on 2n vertices and m <= cn(2) edges have boxicity Omega(m/n).

Codes with Locality for Two Erasures

In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, parity-check computations. By a local parity-check computation, we mean recovery via a single parity-check equation associated with small Hamming weight. Earlier approaches considered recovery in parallel; the sequential approach allows us to potentially construct codes with improved minimum distance. These codes, which we refer to as locally 2-reconstructible codes, are a natural generalization along one direction, of codes with all-symbol locality introduced by Gopalan et al, in which recovery from a single erasure is considered. By studying the generalized Hamming weights of the dual code, we derive upper bounds on the minimum distance of locally 2-reconstructible codes and provide constructions for a family of codes based on Turan graphs, that are optimal with respect to this bound. The minimum distance bound derived here is universal in the sense that no code which permits all-symbol local recovery from 2 erasures can have larger minimum distance regardless of approach adopted. Our approach also leads to a new bound on the minimum distance of codes with all-symbol locality for the single-erasure case.

An enantiodivergent protocol from R-(-)-carvone: synthesis of dihydroagarofuran sesquiterpenoid 1-deacetoxy-ent-orbiculin A

A strategy for achieving enantiodivergency from R-(-)-carvone in the context of synthesis of eudesmanes and dihydroagarofurans is disclosed, which involves, among other things, sequential setting of the C10 quaternary centre and recreation of the desired C7 isopropyl stereochemistry to enter the antipodal series. A synthesis of 1-deacetoxy-ent-orbiculin has been achieved as a demonstration of the effectiveness and applicability of this approach. (C) 2015 Elsevier Ltd. All rights reserved.

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.

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.

Comparison of constructions of irregular Gallager codes

The low-density parity check codes whose performance is closest to the Shannon limit are `Gallager codes' based on irregular graphs. We compare alternative methods for constructing these graphs and present two results. First, we find a `super-Poisson' construction which gives a small improvement in empirical performance over a random construction. Second, whereas Gallager codes normally take N2 time to encode, we investigate constructions of regular and irregular Gallager codes that allow more rapid encoding and have smaller memory requirements in the encoder. We find that these `fast encoding' Gallager codes have equally good performance.

Weaknesses of Margulis and Ramanujan-Margulis low-density parity-check codes

We report weaknesses in two algebraic constructions of low-density parity-check codes based on expander graphs. The Margulis construction gives a code with near-codewords, which cause problems for the sum-product decoder; The Ramanujan-Margulis construction gives a code with low-weight codewords, which produce an error-floor. © 2004 Elsevier B.V.