The Parallel Complexity Of Propagation In Boolean Circuits

We consider the problem of deciding whether the output of a boolean circuit is determined by a partial assignment to its inputs. This problem is easily shown to be hard, i.e., co-Image Image -complete. However, many of the consequences of a partial input assignment may be determined in linear time, by iterating the following step: if we know the values of some inputs to a gate, we can deduce the values of some outputs of that gate. This process of iteratively deducing some of the consequences of a partial assignment is called propagation. This paper explores the parallel complexity of propagation, i.e., the complexity of determining whether the output of a given boolean circuit is determined by propagating a given partial input assignment. We give a complete classification of the problem into those cases that are Image -complete and those that are unlikely to be Image complete.

Reduced complexity two stage vector quantization

We address the issue of complexity for vector quantization (VQ) of wide-band speech LSF (line spectrum frequency) parameters. The recently proposed switched split VQ (SSVQ) method provides better rate-distortion (R/D) performance than the traditional split VQ (SVQ) method, even at the requirement of lower computational complexity. but at the expense of much higher memory. We develop the two stage SVQ (TsSVQ) method, by which we gain both the memory and computational advantages and still retain good R/D performance. The proposed TsSVQ method uses a full dimensional quantizer in its first stage for exploiting all the higher dimensional coding advantages and then, uses an SVQ method for quantizing the residual vector in the second stage so as to reduce the complexity. We also develop a transform domain residual coding method in this two stage architecture such that it further reduces the computational complexity. To design an effective residual codebook in the second stage, variance normalization of Voronoi regions is carried out which leads to the design of two new methods, referred to as normalized two stage SVQ (NTsSVQ) and normalized two stage transform domain SVQ (NTsTrSVQ). These two new methods have complimentary strengths and hence, they are combined in a switched VQ mode which leads to the further improvement in R/D performance, but retaining the low complexity requirement. We evaluate the performances of new methods for wide-band speech LSF parameter quantization and show their advantages over established SVQ and SSVQ methods.

A measure of logical complexity of programs

The research in software science has so far been concentrated on three measures of program complexity: (a) software effort; (b) cyclomatic complexity; and (c) program knots. In this paper we propose a measure of the logical complexity of programs in terms of the variable dependency of sequence of computations, inductive effort in writing loops and complexity of data structures. The proposed complexity mensure is described with the aid of a graph which exhibits diagrammatically the dependence of a computation at a node upon the computation of other (earlier) nodes. Complexity measures of several example programs have been computed and the related issues have been discussed. The paper also describes the role played by data structures in deciding the program complexity.

On the complexity of finding stopping set size in Tanner Graphs

The problem of determining whether a Tanner graph for a linear block code has a stopping set of a given size is shown to be NT-complete.

A Low-Complexity Algorithm for Intrusion Detection in a PIR-Based Wireless Sensor Network

We present a low-complexity algorithm for intrusion detection in the presence of clutter arising from wind-blown vegetation, using Passive Infra-Red (PIR) sensors in a Wireless Sensor Network (WSN). The algorithm is based on a combination of Haar Transform (HT) and Support-Vector-Machine (SVM) based training and was field tested in a network setting comprising of 15-20 sensing nodes. Also contained in this paper is a closed-form expression for the signal generated by an intruder moving at a constant velocity. It is shown how this expression can be exploited to determine the direction of motion information and the velocity of the intruder from the signals of three well-positioned sensors.

Rudiments of complexity theory for scientists and engineers

Complexity theory is an important and growing area in computer science that has caught the imagination of many researchers in mathematics, physics and biology. In order to reach out to a large section of scientists and engineers, the paper introduces elementary concepts in complexity theory in a informal manner, motivating the reader with many examples.

Distributed intrusion detection in the presence of correlated sensor readings: Signal-space and communication-complexity view-point

The problem of sensor-network-based distributed intrusion detection in the presence of clutter is considered. It is argued that sensing is best regarded as a local phenomenon in that only sensors in the immediate vicinity of an intruder are triggered. In such a setting, lack of knowledge of intruder location gives rise to correlated sensor readings. A signal-space view-point is introduced in which the noise-free sensor readings associated to intruder and clutter appear as surfaces f(s) and f(g) and the problem reduces to one of determining in distributed fashion, whether the current noisy sensor reading is best classified as intruder or clutter. Two approaches to distributed detection are pursued. In the first, a decision surface separating f(s) and f(g) is identified using Neyman-Pearson criteria. Thereafter, the individual sensor nodes interactively exchange bits to determine whether the sensor readings are on one side or the other of the decision surface. Bounds on the number of bits needed to be exchanged are derived, based on communication-complexity (CC) theory. A lower bound derived for the two-party average case CC of general functions is compared against the performance of a greedy algorithm. Extensions to the multi-party case is straightforward and is briefly discussed. The average case CC of the relevant greaterthan (CT) function is characterized within two bits. Under the second approach, each sensor node broadcasts a single bit arising from appropriate two-level quantization of its own sensor reading, keeping in mind the fusion rule to be subsequently applied at a local fusion center. The optimality of a threshold test as a quantization rule is proved under simplifying assumptions. Finally, results from a QualNet simulation of the algorithms are presented that include intruder tracking using a naive polynomial-regression algorithm. 2010 Elsevier B.V. All rights reserved.

The complexity of certain incremental code generation problems

This paper looks at the complexity of four different incremental problems. The following are the problems considered: (1) Interval partitioning of a flow graph (2) Breadth first search (BFS) of a directed graph (3) Lexicographic depth first search (DFS) of a directed graph (4) Constructing the postorder listing of the nodes of a binary tree. The last problem arises out of the need for incrementally computing the Sethi-Ullman (SU) ordering [1] of the subtrees of a tree after it has undergone changes of a given type. These problems are among those that claimed our attention in the process of our designing algorithmic techniques for incremental code generation. BFS and DFS have certainly numerous other applications, but as far as our work is concerned, incremental code generation is the common thread linking these problems. The study of the complexity of these problems is done from two different perspectives. In [2] is given the theory of incremental relative lower bounds (IRLB). We use this theory to derive the IRLBs of the first three problems. Then we use the notion of a bounded incremental algorithm [4] to prove the unboundedness of the fourth problem with respect to the locally persistent model of computation. Possibly, the lower bound result for lexicographic DFS is the most interesting. In [5] the author considers lexicographic DFS to be a problem for which the incremental version may require the recomputation of the entire solution from scratch. In that sense, our IRLB result provides further evidence for this possibility with the proviso that the incremental DFS algorithms considered be ones that do not require too much of preprocessing.

Simultaneous MultiStreaming for complexity-effective VLIW architectures

Very Long Instruction Word (VLIW) architectures exploit instruction level parallelism (ILP) with the help of the compiler to achieve higher instruction throughput with minimal hardware. However, control and data dependencies between operations limit the available ILP, which not only hinders the scalability of VLIW architectures, but also result in code size expansion. Although speculation and predicated execution mitigate ILP limitations due to control dependencies to a certain extent, they increase hardware cost and exacerbate code size expansion. Simultaneous multistreaming (SMS) can significantly improve operation throughput by allowing interleaved execution of operations from multiple instruction streams. In this paper we study SMS for VLIW architectures and quantify the benefits associated with it using a case study of the MPEG-2 video decoder. We also propose the notion of virtual resources for VLIW architectures, which decouple architectural resources (resources exposed to the compiler) from the microarchitectural resources, to limit code size expansion. Our results for a VLIW architecture demonstrate that: (1) SMS delivers much higher throughput than that achieved by speculation and predicated execution, (2) the increase in performance due to the addition of speculation and predicated execution support over SMS averages around 12%. The minor increase in performance might not warrant the additional hardware complexity involved, and (3) the notion of virtual resources is very effective in reducing no-operations (NOPs) and consequently reduce code size with little or no impact on performance.

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.

Perspectives on Titanium Science and Technology

The basic framework and - conceptual understanding of the metallurgy of Ti alloys is strong and this has enabled the use of titanium and its alloys in safety-critical structures such as those in aircraft and aircraft engines. Nevertheless, a focus on cost-effectiveness and the compression of product development time by effectively integrating design with manufacturing in these applications, as well as those emerging in bioengineering, has driven research in recent decades towards a greater predictive capability through the use of computational materials engineering tools. Therefore this paper focuses on the complexity and variety of fundamental phenomena in this material system with a focus on phase transformations and mechanical behaviour in order to delineate the challenges that lie ahead in achieving these goals. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The evolution of complexity in social organization-A model using dominance-subordinate behavior in two social wasp species

Dominance and subordinate behaviors are important ingredients in the social organizations of group living animals. Behavioral observations on the two eusocial species Ropalidia marginata and Ropalidia cyathiformis suggest varying complexities in their social systems. The queen of R. cyathiformis is an aggressive individual who usually holds the top position in the dominance hierarchy although she does not necessarily show the maximum number of acts of dominance, while the R. marginata queen rarely shows aggression and usually does not hold the top position in the dominance hierarchy of her colony. In R. marginata, more workers are involved in dominance-subordinate interactions as compared to R. cyathiformis. These differences are reflected in the distribution of dominance-subordinate interactions among the hierarchically ranked individuals in both the species. The percentage of dominance interactions decreases gradually with hierarchical ranks in R. marginata while in R. cyathiformis it first increases and then decreases. We use an agent-based model to investigate the underlying mechanism that could give rise to the observed patterns for both the species. The model assumes, besides some non-interacting individuals, the interaction probabilities of the agents depend on their pre-differentiated winning abilities. Our simulations show that if the queen takes up a strategy of being involved in a moderate number of dominance interactions, one could get the pattern similar to R. cyathiformis, while taking up the strategy of very low interactions by the queen could lead to the pattern of R. marginata. We infer that both the species follow a common interaction pattern, while the differences in their social organization are due to the slight changes in queen as well as worker strategies. These changes in strategies are expected to accompany the evolution of more complex societies from simpler ones.

On the Parameterized Complexity of the Maximum Edge 2-Coloring Problem

We investigate the parameterized complexity of the following edge coloring problem motivated by the problem of channel assignment in wireless networks. For an integer q >= 2 and a graph G, the goal is to find a coloring of the edges of G with the maximum number of colors such that every vertex of the graph sees at most q colors. This problem is NP-hard for q >= 2, and has been well-studied from the point of view of approximation. Our main focus is the case when q = 2, which is already theoretically intricate and practically relevant. We show fixed-parameter tractable algorithms for both the standard and the dual parameter, and for the latter problem, the result is based on a linear vertex kernel.

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 .

Kernelization complexity of possible winner and coalitional manipulation problems in voting

In the POSSIBLE WINNER problem in computational social choice theory, we are given a set of partial preferences and the question is whether a distinguished candidate could be made winner by extending the partial preferences to linear preferences. Previous work has provided, for many common voting rules, fixed parameter tractable algorithms for the POSSIBLE WINNER problem, with number of candidates as the parameter. However, the corresponding kernelization question is still open and in fact, has been mentioned as a key research challenge 10]. In this paper, we settle this open question for many common voting rules. We show that the POSSIBLE WINNER problem for maximin, Copeland, Bucklin, ranked pairs, and a class of scoring rules that includes the Borda voting rule does not admit a polynomial kernel with the number of candidates as the parameter. We show however that the COALITIONAL MANIPULATION problem which is an important special case of the POSSIBLE WINNER problem does admit a polynomial kernel for maximin, Copeland, ranked pairs, and a class of scoring rules that includes the Borda voting rule, when the number of manipulators is polynomial in the number of candidates. A significant conclusion of our work is that the POSSIBLE WINNER problem is harder than the COALITIONAL MANIPULATION problem since the COALITIONAL MANIPULATION problem admits a polynomial kernel whereas the POSSIBLE WINNER problem does not admit a polynomial kernel. (C) 2015 Elsevier B.V. All rights reserved.