Chordal Bipartite Graphs with High Boxicity

The boxicity of a graph G is defined as the minimum integer k such that G is an intersection graph of axis-parallel k-dimensional boxes. Chordal bipartite graphs are bipartite graphs that do not contain an induced cycle of length greater than 4. It was conjectured by Otachi, Okamoto and Yamazaki that chordal bipartite graphs have boxicity at most 2. We disprove this conjecture by exhibiting an infinite family of chordal bipartite graphs that have unbounded boxicity.

Fixed points in a Hopfield model with random asymmetric interactions

We calculate analytically the average number of fixed points in the Hopfield model of associative memory when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. Addition of the antisymmetric part causes an exponential decrease in the total number of fixed points. If the relative strength of the antisymmetric component is small, then its presence does not cause any substantial degradation of the quality of retrieval when the memory loading level is low. We also present results of numerical simulations which provide qualitative (as well as quantitative for some aspects) confirmation of the predictions of the analytic study. Our numerical results suggest that the analytic calculation of the average number of fixed points yields the correct value for the typical number of fixed points.

Some results on the reconstruction problems. p-claw-free, chordal, and p4-reducible graphs

A claw is an induced subgraph isomorphic to K-1,K-3. The claw-point is the point of degree 3 in a claw. A graph is called p-claw-free when no p-cycle has a claw-point on it. It is proved that for p greater than or equal to 4, p-claw-free graphs containing at least one chordless p-cycle are edge reconstructible. It is also proved that chordal graphs are edge reconstructible. These two results together imply the edge reconstructibility of claw-free graphs. A simple proof of vertex reconstructibility of P-4-reducible graphs is also presented. (C) 1995 John Wiley and Sons, Inc.

Structured systems methodology for evaluation of random interruptions in continuous process type manufacturing systems

A structured systems methodology was developed to analyse the problems of production interruptions occurring at random intervals in continuous process type manufacturing systems. At a macro level the methodology focuses on identifying suitable investment policies to reduce interruptions of a total manufacturing system that is a combination of several process plants. An interruption-tree-based simulation model was developed for macroanalysis. At a micro level the methodology focuses on finding the effects of alternative configurations of individual process plants on the overall system performance. A Markov simulation model was developed for microlevel analysis. The methodology was tested with an industry-specific application.

Methods of nonlinear random vibration analysis

The various techniques available for the analysis of nonlinear systems subjected to random excitations are briefly introduced and an overview of the progress which has been made in this area of research is presented. The discussion is mainly focused on the basis, scope and limitations of the solution techniques and not on specific applications.

Lasing in active, sub-mean-free path-sized systems with dense, random, weak scatterers

We report enhanced emission and gain narrowing in Rhodamine 590 perchlorate dye in an aqueous suspension of polystyrene microspheres. A systematic experimental study of the threshold condition for and the gain narrowing of the stimulated emission over a wide range of dye concentrations and scatterer number densities showed several interesting features, even though the transport mean free path far exceeded the system size. The conventional diffusive-reactive approximation to radiative transfer in an inhomogeneously illuminated random amplifying medium, which is valid for a transport mean-free path much smaller than the system size, is clearly inapplicable here. We propose a new probabilistic approach for the present case of dense, random, weak scatterers involving the otherwise rare and ignorable sub-mean-free-path scatterings, now made effective by the high gain in the medium, which is consistent: with experimentally observed features. (C) 1997 Optical Society of America.

The existence of homeomorphic subgraphs in chordal graphs

We establish conditions for the existence, in a chordal graph, of subgraphs homeomorphic to K-n (n greater than or equal to 3), K-m,K-n (m,n greater than or equal to 2), and wheels W-r (r greater than or equal to 3). Using these results, we develop a simple linear time algorithm for testing planarity of chordal graphs. We also show how these results lead to simple polynomial time algorithms for the Fixed Subgraph Homeomorphism problem on chordal graphs for some special classes of pattern graphs.

Improved large-MIMO detection based on damped belief propagation

In this paper, we consider the application of belief propagation (BP) to achieve near-optimal signal detection in large multiple-input multiple-output (MIMO) systems at low complexities. Large-MIMO architectures based on spatial multiplexing (V-BLAST) as well as non-orthogonal space-time block codes(STBC) from cyclic division algebra (CDA) are considered. We adopt graphical models based on Markov random fields (MRF) and factor graphs (FG). In the MRF based approach, we use pairwise compatibility functions although the graphical models of MIMO systems are fully/densely connected. In the FG approach, we employ a Gaussian approximation (GA) of the multi-antenna interference, which significantly reduces the complexity while achieving very good performance for large dimensions. We show that i) both MRF and FG based BP approaches exhibit large-system behavior, where increasingly closer to optimal performance is achieved with increasing number of dimensions, and ii) damping of messages/beliefs significantly improves the bit error performance.

Acyclic Edge-Coloring of Planar Graphs

A proper edge-coloring with the property that every cycle contains edges of at least three distinct colors is called an acyclic edge-coloring. The acyclic chromatic index of a graph G, denoted. chi'(alpha)(G), is the minimum k such that G admits an acyclic edge-coloring with k colors. We conjecture that if G is planar and Delta(G) is large enough, then chi'(alpha) (G) = Delta (G). We settle this conjecture for planar graphs with girth at least 5. We also show that chi'(alpha) (G) <= Delta (G) + 12 for all planar G, which improves a previous result by Fiedorowicz, Haluszczak, and Narayan Inform. Process. Lett., 108 (2008), pp. 412-417].

Freezing of classical fluids in a quenched random potential

The phase diagram of a hard-sphere fluid in the presence of a random pinning potential is studied analytically and numerically. In the analytic work, replicas are introduced for averaging over the quenched disorder, and the hypernetted chain approximation is used to calculate density correlations in the replicated liquid. The freezing transition of the liquid into a nearly crystalline state is studied using a density-functional approach, and the liquid to glass transition is studied using a phenomenological replica symmetry breaking approach. In the numerical work, local minima of a discretized version of the Ramakrishnan-Yussouff free-energy functional are located and the phase diagram in the density-disorder plane is obtained from an analysis of the relative stability of these minima. Both approaches lead to similar results for the phase diagram. The first-order liquid to crystalline solid transition is found to change to a continuous liquid to glass transition as the strength of the disorder is increased above a threshold value.

Minimizing buffer requirements under rate-optimal schedule in regular dataflow networks

Large-grain synchronous dataflow graphs or multi-rate graphs have the distinct feature that the nodes of the dataflow graph fire at different rates. Such multi-rate large-grain dataflow graphs have been widely regarded as a powerful programming model for DSP applications. In this paper we propose a method to minimize buffer storage requirement in constructing rate-optimal compile-time (MBRO) schedules for multi-rate dataflow graphs. We demonstrate that the constraints to minimize buffer storage while executing at the optimal computation rate (i.e. the maximum possible computation rate without storage constraints) can be formulated as a unified linear programming problem in our framework. A novel feature of our method is that in constructing the rate-optimal schedule, it directly minimizes the memory requirement by choosing the schedule time of nodes appropriately. Lastly, a new circular-arc interval graph coloring algorithm has been proposed to further reduce the memory requirement by allowing buffer sharing among the arcs of the multi-rate dataflow graph. We have constructed an experimental testbed which implements our MBRO scheduling algorithm as well as (i) the widely used periodic admissible parallel schedules (also known as block schedules) proposed by Lee and Messerschmitt (IEEE Transactions on Computers, vol. 36, no. 1, 1987, pp. 24-35), (ii) the optimal scheduling buffer allocation (OSBA) algorithm of Ning and Gao (Conference Record of the Twentieth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, Charleston, SC, Jan. 10-13, 1993, pp. 29-42), and (iii) the multi-rate software pipelining (MRSP) algorithm (Govindarajan and Gao, in Proceedings of the 1993 International Conference on Application Specific Array Processors, Venice, Italy, Oct. 25-27, 1993, pp. 77-88). Schedules generated for a number of random dataflow graphs and for a set of DSP application programs using the different scheduling methods are compared. The experimental results have demonstrated a significant improvement (10-20%) in buffer requirements for the MBRO schedules compared to the schedules generated by the other three methods, without sacrificing the computation rate. The MBRO method also gives a 20% average improvement in computation rate compared to Lee's Block scheduling method.

Performance analysis of the random early detection algorithm

In this article we consider a finite queue with its arrivals controlled by the random early detection algorithm. This is one of the most prominent congestion avoidance schemes in the Internet routers. The aggregate arrival stream from the population of transmission control protocol sources is locally considered stationary renewal or Markov modulated Poisson process with general packet length distribution. We study the exact dynamics of this queue and provide the stability and the rates of convergence to the stationary distribution and obtain the packet loss probability and the waiting time distribution. Then we extend these results to a two traffic class case with each arrival stream renewal. However, computing the performance indices for this system becomes computationally prohibitive. Thus, in the latter half of the article, we approximate the dynamics of the average queue length process asymptotically via an ordinary differential equation. We estimate the error term via a diffusion approximation. We use these results to obtain approximate transient and stationary performance of the system. Finally, we provide some computational examples to show the accuracy of these approximations.

Boxicity of Line Graphs

The boxicity of a graph H, denoted by View the MathML source, is the minimum integer k such that H is an intersection graph of axis-parallel k-dimensional boxes in View the MathML source. In this paper we show that for a line graph G of a multigraph, View the MathML source, where Δ(G) denotes the maximum degree of G. Since G is a line graph, Δ(G)≤2(χ(G)−1), where χ(G) denotes the chromatic number of G, and therefore, View the MathML source. For the d-dimensional hypercube Qd, we prove that View the MathML source. The question of finding a nontrivial lower bound for View the MathML source was left open by Chandran and Sivadasan in [L. Sunil Chandran, Naveen Sivadasan, The cubicity of Hypercube Graphs. Discrete Mathematics 308 (23) (2008) 5795–5800]. The above results are consequences of bounds that we obtain for the boxicity of a fully subdivided graph (a graph that can be obtained by subdividing every edge of a graph exactly once).