Complexity of distance paired-domination problem in graphs

Suppose G = (V, E) is a simple graph and k is a fixed positive integer. A subset D subset of V is a distance k-dominating set of G if for every u is an element of V. there exists a vertex v is an element of D such that d(G)(u, v) <= k, where d(G)(u, v) is the distance between u and v in G. A set D subset of V is a distance k-paired-dominating set of G if D is a distance k-dominating set and the induced subgraph GD] contains a perfect matching. Given a graph G = (V, E) and a fixed integer k > 0, the MIN DISTANCE k-PAIRED-DOM SET problem is to find a minimum cardinality distance k-paired-dominating set of G. In this paper, we show that the decision version of MIN DISTANCE k-PAIRED-DOM SET iS NP-complete for undirected path graphs. This strengthens the complexity of decision version Of MIN DISTANCE k-PAIRED-DOM SET problem in chordal graphs. We show that for a given graph G, unless NP subset of DTIME (n(0)((log) (log) (n)) MIN DISTANCE k-PAIRED-Dom SET problem cannot be approximated within a factor of (1 -epsilon ) In n for any epsilon > 0, where n is the number of vertices in G. We also show that MIN DISTANCE k-PAIRED-DOM SET problem is APX-complete for graphs with degree bounded by 3. On the positive side, we present a linear time algorithm to compute the minimum cardinality of a distance k-paired-dominating set of a strongly chordal graph G if a strong elimination ordering of G is provided. We show that for a given graph G, MIN DISTANCE k-PAIRED-DOM SET problem can be approximated with an approximation factor of 1 + In 2 + k . In(Delta(G)), where Delta(G) denotes the maximum degree of G. (C) 2012 Elsevier B.V All rights reserved.

Computing Reeb Graphs as a Union of Contour Trees

The Reeb graph of a scalar function tracks the evolution of the topology of its level sets. This paper describes a fast algorithm to compute the Reeb graph of a piecewise-linear (PL) function defined over manifolds and non-manifolds. The key idea in the proposed approach is to maximally leverage the efficient contour tree algorithm to compute the Reeb graph. The algorithm proceeds by dividing the input into a set of subvolumes that have loop-free Reeb graphs using the join tree of the scalar function and computes the Reeb graph by combining the contour trees of all the subvolumes. Since the key ingredient of this method is a series of union-find operations, the algorithm is fast in practice. Experimental results demonstrate that it outperforms current generic algorithms by a factor of up to two orders of magnitude, and has a performance on par with algorithms that are catered to restricted classes of input. The algorithm also extends to handle large data that do not fit in memory.

EXIT Chart Based Design of Irregular LDPC Codes for Large-MIMO Systems

In this letter, we characterize the extrinsic information transfer (EXIT) behavior of a factor graph based message passing algorithm for detection in large multiple-input multiple-output (MIMO) systems with tens to hundreds of antennas. The EXIT curves of a joint detection-decoding receiver are obtained for low density parity check (LDPC) codes of given degree distributions. From the obtained EXIT curves, an optimization of the LDPC code degree profiles is carried out to design irregular LDPC codes matched to the large-MIMO channel and joint message passing receiver. With low complexity joint detection-decoding, these codes are shown to perform better than off-the-shelf irregular codes in the literature by about 1 to 1.5 dB at a coded BER of 10(-5) in 16 x 16, 64 x 64 and 256 x 256 MIMO systems.

A hybrid RTS-BP algorithm for improved detection of large-MIMO M-QAM signals

Low-complexity near-optimal detection of large-MIMO signals has attracted recent research. Recently, we proposed a local neighborhood search algorithm, namely reactive tabu search (RTS) algorithm, as well as a factor-graph based belief propagation (BP) algorithm for low-complexity large-MIMO detection. The motivation for the present work arises from the following two observations on the above two algorithms: i) Although RTS achieved close to optimal performance for 4-QAM in large dimensions, significant performance improvement was still possible for higher-order QAM (e.g., 16-, 64-QAM). ii) BP also achieved near-optimal performance for large dimensions, but only for {±1} alphabet. In this paper, we improve the large-MIMO detection performance of higher-order QAM signals by using a hybrid algorithm that employs RTS and BP. In particular, motivated by the observation that when a detection error occurs at the RTS output, the least significant bits (LSB) of the symbols are mostly in error, we propose to first reconstruct and cancel the interference due to bits other than LSBs at the RTS output and feed the interference cancelled received signal to the BP algorithm to improve the reliability of the LSBs. The output of the BP is then fed back to RTS for the next iteration. Simulation results show that the proposed algorithm performs better than the RTS algorithm, and semi-definite relaxation (SDR) and Gaussian tree approximation (GTA) algorithms.

Automatic compilation of MATLAB programs for synergistic execution on heterogeneous processors

MATLAB is an array language, initially popular for rapid prototyping, but is now being increasingly used to develop production code for numerical and scientific applications. Typical MATLAB programs have abundant data parallelism. These programs also have control flow dominated scalar regions that have an impact on the program's execution time. Today's computer systems have tremendous computing power in the form of traditional CPU cores and throughput oriented accelerators such as graphics processing units(GPUs). Thus, an approach that maps the control flow dominated regions to the CPU and the data parallel regions to the GPU can significantly improve program performance. In this paper, we present the design and implementation of MEGHA, a compiler that automatically compiles MATLAB programs to enable synergistic execution on heterogeneous processors. Our solution is fully automated and does not require programmer input for identifying data parallel regions. We propose a set of compiler optimizations tailored for MATLAB. Our compiler identifies data parallel regions of the program and composes them into kernels. The problem of combining statements into kernels is formulated as a constrained graph clustering problem. Heuristics are presented to map identified kernels to either the CPU or GPU so that kernel execution on the CPU and the GPU happens synergistically and the amount of data transfer needed is minimized. In order to ensure required data movement for dependencies across basic blocks, we propose a data flow analysis and edge splitting strategy. Thus our compiler automatically handles composition of kernels, mapping of kernels to CPU and GPU, scheduling and insertion of required data transfer. The proposed compiler was implemented and experimental evaluation using a set of MATLAB benchmarks shows that our approach achieves a geometric mean speedup of 19.8X for data parallel benchmarks over native execution of MATLAB.

Analysing modifica-tions in the synthesis of multiple state mechanical devices using configuration space and topology graphs

Automated synthesis of mechanical designs is an important step towards the development of an intelligent CAD system. Research into methods for supporting conceptual design using automated synthesis has attracted much attention in the past decades. In our research, ten experimental studies are conducted to find out how designers synthesize solution concepts for multi-state mechanical devices. The designers are asked to think aloud, while carrying out the synthesis. These design synthesis processes are video recorded. It has been found that modification of kinematic pairs and mechanisms is the major activity carried out by all the designers. This paper presents an analysis of these synthesis processes using configuration space and topology graph to identify and classify the types of modifications that take place. Understanding of these modification processes and the context in which they happened is crucial to develop a system for supporting design synthesis of multiple state mechanical devices that is capable of creating a comprehensive variety of solution alternatives.

Phase synchronization in brain networks derived from correlation between probabilities of recurrences in functional MRI data

It is increasingly being recognized that resting state brain connectivity derived from functional magnetic resonance imaging (fMRI) data is an important marker of brain function both in healthy and clinical populations. Though linear correlation has been extensively used to characterize brain connectivity, it is limited to detecting first order dependencies. In this study, we propose a framework where in phase synchronization (PS) between brain regions is characterized using a new metric ``correlation between probabilities of recurrence'' (CPR) and subsequent graph-theoretic analysis of the ensuing networks. We applied this method to resting state fMRI data obtained from human subjects with and without administration of propofol anesthetic. Our results showed decreased PS during anesthesia and a biologically more plausible community structure using CPR rather than linear correlation. We conclude that CPR provides an attractive nonparametric method for modeling interactions in brain networks as compared to standard correlation for obtaining physiologically meaningful insights about brain function.

Generalized distributive law for ML decoding of space-time block codes

The problem of designing good space-time block codes (STBCs) with low maximum-likelihood (ML) decoding complexity has gathered much attention in the literature. All the known low ML decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast-decodable (conditionally multigroup decodable) structure of a code. We refer to this well-known technique of decoding STBCs as conditional ML (CML) decoding. In this paper, we introduce a new framework to construct ML decoders for STBCs based on the generalized distributive law (GDL) and the factor-graph-based sum-product algorithm. We say that an STBC is fast GDL decodable if the order of GDL decoding complexity of the code, with respect to the constellation size, is strictly less than M-lambda, where lambda is the number of independent symbols in the STBC. We give sufficient conditions for an STBC to admit fast GDL decoding, and show that both multigroup and conditionally multigroup decodable codes are fast GDL decodable. For any STBC, whether fast GDL decodable or not, we show that the GDL decoding complexity is strictly less than the CML decoding complexity. For instance, for any STBC obtained from cyclic division algebras which is not multigroup or conditionally multigroup decodable, the GDL decoder provides about 12 times reduction in complexity compared to the CML decoder. Similarly, for the Golden code, which is conditionally multigroup decodable, the GDL decoder is only half as complex as the CML decoder.

Performance improvement of short-length regular low-density parity-check codes with low-complexity post-processing

It is well known that extremely long low-density parity-check (LDPC) codes perform exceptionally well for error correction applications, short-length codes are preferable in practical applications. However, short-length LDPC codes suffer from performance degradation owing to graph-based impairments such as short cycles, trapping sets and stopping sets and so on in the bipartite graph of the LDPC matrix. In particular, performance degradation at moderate to high E-b/N-0 is caused by the oscillations in bit node a posteriori probabilities induced by short cycles and trapping sets in bipartite graphs. In this study, a computationally efficient algorithm is proposed to improve the performance of short-length LDPC codes at moderate to high E-b/N-0. This algorithm makes use of the information generated by the belief propagation (BP) algorithm in previous iterations before a decoding failure occurs. Using this information, a reliability-based estimation is performed on each bit node to supplement the BP algorithm. The proposed algorithm gives an appreciable coding gain as compared with BP decoding for LDPC codes of a code rate equal to or less than 1/2 rate coding. The coding gains are modest to significant in the case of optimised (for bipartite graph conditioning) regular LDPC codes, whereas the coding gains are huge in the case of unoptimised codes. Hence, this algorithm is useful for relaxing some stringent constraints on the graphical structure of the LDPC code and for developing hardware-friendly designs.

Modelling and analysis of new coolstreaming for P2P IPTV

Peer to peer networks are being used extensively nowadays for file sharing, video on demand and live streaming. For IPTV, delay deadlines are more stringent compared to file sharing. Coolstreaming was the first P2P IPTV system. In this paper, we model New Coolstreaming (newer version of Coolstreaming) via a queueing network. We use two time scale decomposition of Markov chains to compute the stationary distribution of number of peers and the expected number of substreams in the overlay which are not being received at the required rate due to parent overloading. We also characterize the end-to-end delay encountered by a video packet received by a user and originated at the server. Three factors contribute towards the delay. The first factor is the mean shortest path length between any two overlay peers in terms of overlay hops of the partnership graph which is shown to be O (log n) where n is the number of peers in the overlay. The second factor is the mean number of routers between any two overlay neighbours which is seen to be at most O (log N-I) where N-I is the number of routers in the internet. Third factor is the mean delay at a router in the internet. We provide an approximation of this mean delay E W]. Thus, the mean end to end delay in New Coolstreaming is shown to be upper bounded by O (log E N]) (log N-I) E (W)] where E N] is the mean number of peers at a channel.

Classification, representation, and automatic extraction of deformation features in sheet metal parts

This paper presents classification, representation and extraction of deformation features in sheet-metal parts. The thickness is constant for these shape features and hence these are also referred to as constant thickness features. The deformation feature is represented as a set of faces with a characteristic arrangement among the faces. Deformation of the base-sheet or forming of material creates Bends and Walls with respect to a base-sheet or a reference plane. These are referred to as Basic Deformation Features (BDFs). Compound deformation features having two or more BDFs are defined as characteristic combinations of Bends and Walls and represented as a graph called Basic Deformation Features Graph (BDFG). The graph, therefore, represents a compound deformation feature uniquely. The characteristic arrangement of the faces and type of bends belonging to the feature decide the type and nature of the deformation feature. Algorithms have been developed to extract and identify deformation features from a CAD model of sheet-metal parts. The proposed algorithm does not require folding and unfolding of the part as intermediate steps to recognize deformation features. Representations of typical features are illustrated and results of extracting these deformation features from typical sheet metal parts are presented and discussed. (C) 2013 Elsevier Ltd. All rights reserved.

Sufficient conditions for formation of a network topology by self-interested agents

Networks such as organizational network of a global company play an important role in a variety of knowledge management and information diffusion tasks. The nodes in these networks correspond to individuals who are self-interested. The topology of these networks often plays a crucial role in deciding the ease and speed with which certain tasks can be accomplished using these networks. Consequently, growing a stable network having a certain topology is of interest. Motivated by this, we study the following important problem: given a certain desired network topology, under what conditions would best response (link addition/deletion) strategies played by self-interested agents lead to formation of a pairwise stable network with only that topology. We study this interesting reverse engineering problem by proposing a natural model of recursive network formation. In this model, nodes enter the network sequentially and the utility of a node captures principal determinants of network formation, namely (1) benefits from immediate neighbors, (2) costs of maintaining links with immediate neighbors, (3) benefits from indirect neighbors, (4) bridging benefits, and (5) network entry fee. Based on this model, we analyze relevant network topologies such as star graph, complete graph, bipartite Turan graph, and multiple stars with interconnected centers, and derive a set of sufficient conditions under which these topologies emerge as pairwise stable networks. We also study the social welfare properties of the above topologies.

On Computing Amplitude, Phase, and Frequency Modulations Using a Vector Interpretation of the Analytic Signal

The amplitude-modulation (AM) and phase-modulation (PM) of an amplitude-modulated frequency-modulated (AM-FM) signal are defined as the modulus and phase angle, respectively, of the analytic signal (AS). The FM is defined as the derivative of the PM. However, this standard definition results in a PM with jump discontinuities in cases when the AM index exceeds unity, resulting in an FM that contains impulses. We propose a new approach to define smooth AM, PM, and FM for the AS, where the PM is computed as the solution to an optimization problem based on a vector interpretation of the AS. Our approach is directly linked to the fractional Hilbert transform (FrHT) and leads to an eigenvalue problem. The resulting PM and AM are shown to be smooth, and in particular, the AM turns out to be bipolar. We show an equivalence of the eigenvalue formulation to the square of the AS, and arrive at a simple method to compute the smooth PM. Some examples on synthesized and real signals are provided to validate the theoretical calculations.

Generalized distributive law for ML decoding of STBCs: further results

The problem of designing good Space-Time Block Codes (STBCs) with low maximum-likelihood (ML) decoding complexity has gathered much attention in the literature. All the known low ML decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast-decodable (conditionally multigroup decodable) structure of a code. We refer to this well known technique of decoding STBCs as Conditional ML (CML) decoding. In [1], we introduced a framework to construct ML decoders for STBCs based on the Generalized Distributive Law (GDL) and the Factor-graph based Sum-Product Algorithm, and showed that for two specific families of STBCs, the Toepltiz codes and the Overlapped Alamouti Codes (OACs), the GDL based ML decoders have strictly less complexity than the CML decoders. In this paper, we introduce a `traceback' step to the GDL decoding algorithm of STBCs, which enables roughly 4 times reduction in the complexity of the GDL decoders proposed in [1]. Utilizing this complexity reduction from `traceback', we then show that for any STBC (not just the Toeplitz and Overlapped Alamouti Codes), the GDL decoding complexity is strictly less than the CML decoding complexity. For instance, for any STBC obtained from Cyclic Division Algebras that is not multigroup or conditionally multigroup decodable, the GDL decoder provides approximately 12 times reduction in complexity compared to the CML decoder. Similarly, for the Golden code, which is conditionally multigroup decodable, the GDL decoder is only about half as complex as the CML decoder.

Bipartite Powers of k-chordal Graphs

Let k be an integer and k >= 3. A graph G is k-chordal if G does not have an induced cycle of length greater than k. From the definition it is clear that 3-chordal graphs are precisely the class of chordal graphs. Duchet proved that, for every positive integer m, if G m is chordal then so is G(m+2). Brandst `` adt et al. in Andreas Brandsadt, Van Bang Le, and Thomas Szymczak. Duchet- type theorems for powers of HHD- free graphs. Discrete Mathematics, 177(1- 3): 9- 16, 1997.] showed that if G m is k - chordal, then so is G(m+2). Powering a bipartite graph does not preserve its bipartitedness. In order to preserve the bipartitedness of a bipartite graph while powering Chandran et al. introduced the notion of bipartite powering. This notion was introduced to aid their study of boxicity of chordal bipartite graphs. The m - th bipartite power G(m]) of a bipartite graph G is the bipartite graph obtained from G by adding edges (u; v) where d G (u; v) is odd and less than or equal to m. Note that G(m]) = G(m+1]) for each odd m. In this paper we show that, given a bipartite graph G, if G is k-chordal then so is G m], where k, m are positive integers with k >= 4