Two-level Networks Research Articles

New pricing strategies and an effective exact solution framework for profit-oriented ring arborescence problems

We study novel solution methods for a class of network optimization problems that find application in strategic planning of telecommunication infrastructure. These directed network design models are used to compute centralized two-level networks under capacity constraints: Circuits on the inner level and directed trees in the periphery.We develop non-compact arc-based and set-packing formulations and integrate cuts to strengthen polyhedral descriptions of their relaxations. Theoretical results on polyhedral structure are provided that serve as the foundation of our branch-and-cut-and-price methods. For the column generation component, we introduce new relaxations of the pricing problem that are based on not necessarily elementary ring arborescences: q-d-Steiner-arb and ng-ring-Steiner-arbs. These models are related to q-arbs and ng-route relaxations known to be state-of-the-art for related network optimization models including vehicle routing. Our effective algorithmic framework incorporates iterated local search based primal heuristics and exact pricing strategies that can be applied to all considered model variants and related network design problems.The novel methods clearly outperform existing approaches from the literature regarding both solution time and solution quality. In a computational study, we show that our algorithms are capable of closing most optimality gaps for unsolved literature instances with up to 51 vertices. Furthermore, we provide results for new larger instances with up to 101 vertices.

Network Decoding Against Restricted Adversaries

We initiate the study of the one-shot capacity of communication (coded) networks with an adversary having access only to a proper subset of the network edges. We introduce the Diamond Network as a minimal example to show that known cut-set bounds are not sharp in general, and that their non-sharpness comes precisely from restricting the action of the adversary to a region of the network. We give a capacity-achieving scheme for the Diamond Network that implements an adversary detection strategy. We also show that linear network coding does not suffice in general to achieve capacity, proving a strong separation result between the one-shot capacity and its linear version. We then give a sufficient condition for tightness of the Singleton Cut-Set Bound in a family of two-level networks. Finally, we discuss how the presence of nodes that do not allow local encoding and decoding does or does not affect the one-shot capacity.

Analysis of Two-Layer Resource Supply Flow Networks

The problem of controlling resource flows in two-level networks with a tree structure simulated by a simplified radial structure at each level is considered. A resource flow vector to end consumers is taken as the maximized functional characteristic. Two flow control strategies are analyzed to obtain a Pareto optimal solution based on a weighted leximin rule. The first strategy, called the equal-share resource allocation, is based on the idea of equalizing the ratio of the delivered resource volume to the maximum possible resource volume for the given node for the given network capacity. The second strategy, which ensures that resources are allocated equally, is based on the idea of equalizing the ratio of the delivered resource volume to the required resource volume. In the case of unknown requirements, it is proposed to focus on the strategy that ensures equal allocation. Both strategies are described in two variants: optimization at the main level with the further additional optimization in each allocation network and direct optimization without an intermediate level. It is shown that the solutions are different. Their properties are studied. The possibility of combining different rules is investigated. A model example is presented.

Semi-Automatic Extraction of Training Examples From Sensor Readings for Fall Detection and Posture Monitoring

While inexpensive wearable motion-sensing devices have shown great promise for fall detection and posture monitoring, two major problems still exist and have to be solved: 1) a framework for the development of firmware and 2) software to make intelligent decisions. We address both the problems. We propose a generic framework for developing the firmware. We also demonstrate that the k-means clustering algorithm can semi-automatically extract training examples from motion data. Moreover, we trained and evaluated several one- and two-level classification networks to monitor non-fall activities and to detect fall events. The proposed classification networks are the combinations of neural networks and softmax regression. These networks are trained offline with examples extracted by our proposed method. The cross-validation of trained two-level networks shows 100% accuracy for non-fall activities and fall events. The data sets for training and testing have been collected using the devices we assembled with four off-the-shelf components. We have programmed them using a prototype of our proposed framework. The data sets include seven types of non-fall activities and four types of fall events. This paper advances the state of the art for the development and training of wearable devices for monitoring non-fall activities and detecting fall events.

Hierarchical Survivable Network Design Problems

We address the problem of designing two-level networks protected against single edge failures. A set of nodes must be partitioned into terminals and hubs, hubs must be connected through a backbone network, and terminals must be assigned to hubs and connected to them through access networks, being the objective to minimize the total cost. We consider two survivable structures, two-edge connected (2EC) networks and rings, in both levels of the network. We present an integer programming formulation for these problems, solve them using a branch-and-cut algorithm, and show some computational results.

Level-Based Approach to Public Transport Network Planning

The public transport network level is defined and is used to describe the performance and future improvement of the public transport system in Zurich, Switzerland. A public transport level is a specific type of service designed to serve a particular market. “Service” is defined as a combination of vehicles, infrastructure, and operating characteristics. A pure level occurs when the service is targeted specifically at one particular market. A hybrid level occurs when a service is targeted to serve several markets. Urban travel is generally described as three markets: short, inter mediate, and long-distance trips. Consequently many cities have developed three-level public transport networks: surface buses and trams to serve short trips, rapid rail to serve intermediate trips, and regional rail to serve longer-distance trips. Often, by design or for historic reasons, cities have additional levels, fewer levels, levels that are not precisely matched to their markets, or all three. For example, two-level networks are often found in medium-sized cities. Their advantage is lower costs, and their main disadvantage is a mismatch between transport mode and market that manifests itself in capacity limitations. The level concept to help analyze and plan public transport service is useful because it focuses attention on matching service qualities to markets. This approach, used here to analyze the success of the public transport system of Zurich, Switzerland, and to provide a structure for planning improvements that will be needed to meet rapidly increasing public transport demand, could help other cities design or redesign their public transport systems to be more attractive and efficient. More specifically, the approach could show how two-level public transport networks would be a viable option for medium-sized cities and large cities with dispersed settlement patterns.

Dominating problems in swapped networks

Swapped Networks (SNs) are a family of two-level interconnection networks, suitable for constructing large parallel and distributed systems. In this paper, the Minimum Dominating Set (MDS) problem and the Minimum Connected Dominating Set (MCDS) problem in SNs are investigated based on the connectivity rule of SNs. We prove the two problems in SNs are NP-hard, and present two efficient algorithms for building dominating sets and connected dominating sets in SNs. The proposed algorithms use as input a given (connected) dominating set of the factor network, and yield a good approximation of an MDS or MCDS for the SN provided that the input is a good approximation of an MDS or MCDS for the factor network. We also derive several non-trivial bounds on the (connected) domination parameters of SNs. We believe this work is of theoretical interest in graph theory since SNs form a family of graphs. It may also motivate further research on dominating problems in SNs with their potential applications.

Fault Diagnosis on Transmission System of Wind Turbines Based on Wavelet Packet Transform and RBF Neural Networks

Wind turbine transmission system with abundant fault feature and variable types, the vibration signal was a carrier of fault features and it can reflect most of the fault information in the wind turbine transmission system. As there were a large number of transient and non-stationary signals accompany with the vibration signals, so wavelet packet transform was adopted for feature extraction. As RBF Neural network has a strong nonlinear mapping ability and self-adaptability, so it was introduced to the diagnosis system for network training, the neural networks structure and learning algorithm was presented, which could enhance the accuracy of diagnosis. The two-level neural networks recognition method was proposed, first level for fault classification and second level for fault diagnosis. The example shows that this method can be effectively applied to transmission system of wind turbine fault diagnosis with wavelet packet algorithm for fault feature extraction and RBF neural network for pattern recognition.

Application of genetic algorithm in computing the tradeoffs between power consumption versus delay in digital integrated circuit design

This paper presents a novel methodology to obtain the entire power consumption versus delay tradeoff curve for the critical paths of a combinational logic circuit in a very efficient way using the genetic algorithm (GA). In order to evaluate the proposed algorithm the most representative set of two-level and multi-level networks from the MCNC91 benchmark suite were processed. The required computational effort, measured in terms of CPU time, is several times better for the proposed GA optimization technique than liner programming (LP) technique. On the other hand, the optimal design points obtained by the GA and LP techniques are very close to each other to within 0.3%.

Comprehensive partial decoding approach for two-level relay networks

Partial decoding scheme is a scheme in which each relay decodes only part of the transmitted message. Obviously, the achievable rates proposed by the partial decoding scheme subsume the achievable rates proposed by the full decoding scheme. The other motivation of using partial decoding scheme is that there are some special classes of relay networks such as semi-deterministic and orthogonal relay networks such that their capacities are obtained via this scheme. The authors propose a comprehensive partial decoding scheme based on regular encoding/sliding window decoding analysis to propose a new achievable rate for two-level relay networks. In contrast with the previously proposed methods, here the authors consider all possible partial decoding states that can occur between the different parts of the messages of the source and the relays in a two-level relay network. In this way, the common and private parts of the message transmitted by the source are defined to be decoded by the appropriate relays. Moreover, in the proof, the authors take advantage of regular encoding/sliding window decoding scheme that has superiorities to regular encoding/backward decoding and irregular encoding/random partitioning, in having less delay and yielding higher rates, respectively.

Complexity of probabilistic reasoning in directed-path singly-connected Bayes networks

Directed-path (DP) singly-connected Bayesian networks are an interesting special case that, in particular, includes both polytrees and two-level networks. We analyze the computational complexity of these networks. The prediction problem is shown to be easy, as standard message passing can perform correct updating. However, diagnostic reasoning is hard even for DP singly-connected networks. In addition, finding the most-probable explanation (MPE) is hard, even without evidence. Finally, complexity of nearly DP singly-connected networks is analyzed.

Hierarchical Networks for Optical Communications

ShuffleNet and de Bruijn networks have been proposed as multihop lightwave networks based on wavelength division multiplexing (WDM). With multihop lightwave networks, few fixed wavelength transmitters/receivers are assigned to each user, eliminating the need for wavelength agility and pretransmission coordination. These networks have been shown to be very effective for uniform traffic. For communications with high locality, we propose two-level hierarchical networks. At the first level, each cluster of users can be connected either via a ShuffleNet (SH) or a de Bruijn network (dB). At the second level, all the clusters in the system can be connected by two rings in opposite directions (SH/Ring and dB/Ring), a de Bruijn network (dB/dB), or a ShuffleNet (SH/SH). The performance of ShuffleNet, de Bruijn networks, and the hierarchical networks SH/Ring, dB/Ring, dB/dB, and SH/SH is analyzed. For communications with a high locality, the hierarchical networks are shown to be very effective.

Combinatorial properties of two-level hypernet networks

The purpose of the paper is to investigate combinatorial properties of the hypernet network. The hypernet network owns two structural advantages: expansibility and equal degree. In addition, it was shown to be efficient in both communication and computation. Since the number of nodes contained in the hypernet network increases very rapidly with expansion level, we emphasize the hypernet network of two levels (denoted by HN(d, 2)) with a practical view. Recently, combinatorial properties such as container (i.e., node-disjoint paths), wide diameter, and fault diameter have received much attention due to their increasing importance and applications in networks. The following results are obtained for HN(d, 2): (1) best containers with width d-1, (2) containers with (maximum) width d, (3) the (d-1)-wide diameter, (4) the d-wide diameter, (5) the (d-2)-fault diameter, and (6) the (d-1)-fault diameter. More specifically, between every two nodes of HN(d, 2), d (or d-1) packets can be transmitted simultaneously with at most D+2 (or D+1) parallel steps, where D=2d+1 is the diameter of HN(d, 2). Besides, the diameter of HN(d, 2) will increase by at most two (or one), if there are at most d-1 (or d-2) node faults. Our results reveal that HN(d, 2) is not only efficient in parallel transmission, but robust in fault tolerance.

Topological properties and algorithms for two-level hypernet networks

Although many networks have been proposed as the topology of a large-scale parallel and distributed system, most of them are neither expansible nor of equal degree. A network with these two properties will gain the advantages of easy implementation and low cost when it is manufactured. The hypernet, which was proposed by Hwang and Ghosh, represents a family of recursively scalable networks that are both expansible and of equal degree. In addition to the two merits, the hypernet has proven efficient for communication and computation. But, unfortunately, most topological properties and the problem of shortest-path routing for the hypernet are still unsolved. The reason is that the structure of the hypernet is complex and asymmetric, and, especially, no mathematical description was given before. In this paper, considering current hardware restrictions, we concentrate our effort on the hypernet of moderate size. We first give a concise mathematical definition for the hypernet and then solve the following problems for the hypernet of two levels: (1) shortest-path routing, (2) diameter, (3) connectivity, (4) minimum-height spanning trees, and (5) embedding of rings, tori, and hypercubes. © 1998 John Wiley & Sons, Inc. Networks 31:105–118, 1998

On the boolean-quadric packinguncapacitated facility-location polytope

We introduce and study the boolean-quadric uncapacitated packing facility-location polytope BQPUFLP(m, n), which is a model for uncapacitated facility-location problems, with m facilities and n customers, in which there are fixed costs associated with the operation of pairs of facilities. This problem arises in the design of two-level telecommunication networks in which the embedded backbone network is full-meshed and the local networks are of star type. We study the facial structure of BQPUFLP(m, n); in particular, we demonstrate that every facet of the boolean-quadric polytope BQP(m) is a facet of BQPUFLP(m, n),we introduce some facets of BQPUFLP(m, n) that are not related to BQP(m), and we provide a complete description of the facets of BQPUFLP(m, n) when m = 3. Finally, we describe a cutting-plane algorithm based on our results, and we report on the results of computational experiments on problems with m = 50 facilities and n = 1000 customers.

Optical cellular logic two-level networks for morphological image processing

A cellular logic two-level network architecture is proposed for binary image processing. Any binary morphological image processing function can be synthesized into two-level switching functions and executed by two-level networks by the simply repeated use of hardware, and the logic functions of some important image processing are derived in SP form or PS form. Optoelectronic implementation system and experimental results are shown.

A method for minimization design of two-level logic networks using multiplexer universal logic modules

A decomposition approach of the combinational functions is discussed. A design method, by which the minimization or near minimization of two-level combinational network can be obtained, is presented for a combinational function realized by using multiplexer universal logic modules. Using the method, the automated synthesis of the combinational functions can be accomplished on a computer.

Graph representation of logic functions to design two-level MOS networks

The design problem of two-level MOS networks with a minimum number of cells is reduced to the covering problem of graphs with a minimum number of cliques. When every node of the graph corresponds to a minterm, an algorithm which generates an MOS network with a minimum number of cells is presented. The time complexity of this algorithm is O(M)2, where M is the number of minterms. When every node of the graph corresponds to a prime implicant, a procedure which generates near optimum solutions by selecting prime implicants with special properties is presented. About 2 percent of designed networks for four-variable functions are not minimal ones.

Optimal design of hazard-free and easily testable logic networks

The problem of designing optimal two-level static-logic hazard-free combinational networks is considered from a graph theoretic viewpoint. Two algorithms are presented, one of which generates the design with minimum number of appearances of extra control inputs with which the circuit is to be augmented, and the other generates a design with an absolute minimum number of distinct control inputs. The proposed methods are guaranteed to produce a design with minimum changes in the circuit, unlike other existing methods. The detection of stuck-at and bridging faults in such networks is also discussed from the viewpoint of test set generation and syndrome testing.

Identification of Equivalent Faults in Logic Networks

The properties of combinational logic functions and networks that influence equivalence among stuck-type faults are investigated. It is shown that the equivalence of certain types of faults depends only on the function being realized. For instance, the fault classes among primary input/output faults are of this type. It is shown that every irredundant realization of the two-variable EXCLUSIVE-OR function has a unique set of ten fault classes. A fault class F in a module M contained in a network N is called intrinsic, if F can be determined from M alone, i. e., F is independent of N. Using the concepts of intrinsic equivalence and inversion parity, conditions for the equivalence and nonequivalence of two fault classes are obtained. These results are applied to the problem of equivalence identification in two-level logic networks where they provide a substantial reduction in the amount of computation required.