Maximum Weight Matching Algorithm Research Articles

A Novel Signal-Scheduling Algorithm With Quality-of-Service Provisioning for an Isolated Intersection

There have been countless efforts directed toward efficiently controlling the flow of vehicular traffic through an intersection. This paper describes an algorithm designed for the signal control problem that employs concepts drawn from the field of packet switching in computer networks. The novel method proposed utilizes a maximal weight matching algorithm to minimize the queue sizes at each approach, yielding significantly lower average vehicle delay through the intersection. Of particular interest are scenarios in which differentiated services are offered to vehicle classes with differing priorities. Lyapunov function-based analysis is provided, deriving the conditions under which the system is guaranteed to be stable. The algorithm is compared to an optimized fixed-time controller and a vehicle-actuated controller using the VISSIM traffic simulation environment. Simulation results demonstrate the performance gain obtained when using the proposed scheme, particularly in the scenario in which vehicle routes are unequally distributed, and multiple classes of service are desired.

Efficient Algorithms for Variants of Weighted Matching and Assignment Problems

Obtaining a matching in a graph satisfying a certain objective is an important class of graph problems. Matching algorithms have received attention for several decades. However, while there are efficient algorithms to obtain a maximum weight matching, not much is known about the maximum weight maximum cardinality, and maximum cardinality maximum weight matching problems for general graphs. Our contribution in this work is to show that for bounded weight input graphs one can obtain an algorithm for both maximum weight maximum cardinality (for real weights), and maximum cardinality maximum weight matching (for integer weights) by modifying the input and running the existing maximum weight matching algorithm. Also, given the current state of the art in maximum weight matching algorithms, we show that, for bounded weight input graphs, both maximum weight maximum cardinality, and maximum cardinality maximum weight matching have algorithms of similar complexities to that of maximum weight matching. Subsequently, we also obtain approximation algorithms for maximum weight maximum cardinality, and maximum cardinality maximum weight matching.

Stability of a frame-based oldest-cell-first maximal weight matching algorithm

Input-queued cell switches employing the oldest-cell-first (OCF) policy have been shown to yield low mean delay characteristics. Moreover, it has been proven that OCF is stable for admissible traffic conditions when executed with a scheduling speedup of 2. However, as link speeds increase, the computational complexity of these algorithms limits their applicability in high port-density switches and routers. To address the scalability issue, we describe a Frame-Based Maximal Weight Matching (FMWM) algorithm, employing OCF as queue weights, in which a new scheduling decision is issued once every several cell times. Between scheduling decisions, the configuration of the crossbar switch remains unchanged. We further extend the analysis to address the case of multiple classes of service, and prove that the algorithm is stable with an internal buffer transfer speedup of 2, thereby significantly relaxing the timing constraints imposed on the scheduling process.

A distributed switch scheduling algorithm

The maximum weight matching algorithm is a high-performance scheduling algorithm for cross-bar switches. It is known that it performs optimally under heavy loads. However, its centralized nature and high computational complexity limit the algorithm’s applicability. This paper presents a randomized algorithm for distributed switch scheduling that is capable of delivering high throughput.

Maximum weight matching and genetic algorithm for fixed-shape facility layout problem

To achieve efficient facility design, the problem of finding an initial slicing tree of a complete graph may influence the layout solutions in many ways. We introduce a maximum weight-matching algorithm to generate the slicing tree, which is used as an initial solution. This initial solution produces modifications to generate alternative layouts for further selection. The system employs a genetic algorithm (GA) as the search engine with a relationship weight function to obtain good solutions. The model is proposed to solve a fixed-shape layout problem. The research has made contributions to two areas. First, it defines a quality function for the clustering technique to generate an initial slicing tree. Second, it designs a process for generating layout alternatives that can take predetermined location constraints and weights based on relationships among facilities into consideration. We compare our initial slicing tree GA with other approaches in the literature. In addition, computational results to demonstrate the performance characteristics of our algorithm are also evaluated.

Low complexity, stable scheduling algorithms for networks of input queued switches with no or very low speed-up

The delay and throughput characteristics of a packet switch depend mainly on the queueing scheme and the scheduling algorithm deployed at the switch. Early research on scheduling algorithms has mainly focused on maximum weight matching scheduling algorithms. It is known that maximum weight matching algorithms guarantee the stability of input-queued switches, but are impractical due to their high computational complexity. Later research showed that the less complex maximal matching algorithms can stabilize input-queued switches when they are deployed with a speed-up of two. For practical purposes, neither a high computational complexity nor a speed-up of two is desirable.In this paper, we investigate the application of matching algorithms that approximate maximum weight matching algorithms to scheduling problems. We show that while having a low computational complexity, they guarantee the stability of input queued switches when they are deployed with a moderate speed-up.In particular, we show that the improve_matching algorithm stabilizes input-queued switches when it is deployed with a speed-up of 3<over>2+ε.In a second step, we further improve on these results by proposing a class of maximal weight matching algorithms that stabilize an input-queued switch without any speed-up.Whereas initial research has only focused on scheduling algorithms that guarantee the stability of a single switch, recent work has shown how scheduling algorithms for single switches can be modified in order to design distributed scheduling algorithms that stabilize networks of input-queued switches. Using those results, we show that the switching algorithms proposed in this paper do not only stabilize a single switch, but also networks of input-queued switches.

Stability of a frame-based maximal weight matching algorithm with transfer speedup

It has been shown that maximal size matching algorithms for input-queued switches are stable under any admissible traffic conditions with a scheduling speedup of 2. However, as link speeds increase, the computational complexity of these algorithms limits their applicability in high port-density switches and routers. In this letter we describe a Frame-Based Maximal Weight Matching (FMWM) algorithm in which a new scheduling decision is issued once every several cell times. Between scheduling decisions, the configuration of the crossbar switch remains unchanged. We prove that the FMWM algorithm is stable with an internal buffer transfer speedup of 2, thereby significantly relaxing the timing constraints on the scheduling process. Simulation results illustrate the impact of the algorithm on the average cell delay for different traffic scenarios.

Cell switching versus packet switching in input-queued switches

Input Queued (IQ) switches have been well studied in the past two decades by researchers. The main problem concerning IQ switches is scheduling the switching fabric in order to transfer packets from input ports to output ports. Scheduling is relatively easier when all packets are of the same size. However, in practice, packets are of variable length. In the current implementation of switches, variable length packets are segmented into fixed length packets-also knowns as cells-for the purpose of scheduling. However, such cell-based switching comes with some significant disadvantages: (a) loss of bandwidth due to the existence of incomplete cells; and (b) additional overhead of segmentation of packets and re-assembly of cells. This is a strong motivation to study packet-based scheduling, i.e., scheduling the transfer of packets without segmenting them. The problem of packet scheduling was first considered by Marsan et al. They showed that under any admissible Bernoulli IID (independent and identically distributed) arrival traffic, a simple modification of the Maximum Weight Matching (MWM) algorithm achieves 100% throughput. In this paper, we first show that no work-conserving (i.e., maximal) packet-based algorithm is stable for arbitrary admissible arrival processes. Thus, the results of Marsan et al. are strongly dependent on the arrival distribution. Next, we propose a new class of waiting algorithms. We show that the waiting-MWM algorithm is stable for any admissible traffic using the fluid limit technique. We would like to note that the algorithms presented in this paper are distribution independent or universal. The algorithms and proof methods of this paper may be useful in the context of other scheduling problems.

DiANNA: a web server for disulfide connectivity prediction

Correctly predicting the disulfide bond topology in a protein is of crucial importance for the understanding of protein function and can be of great help for tertiary prediction methods. The web server outputs the disulfide connectivity prediction given input of a protein sequence. The following procedure is performed. First, PSIPRED is run to predict the protein's secondary structure, then PSIBLAST is run against the non-redundant SwissProt to obtain a multiple alignment of the input sequence. The predicted secondary structure and the profile arising from this alignment are used in the training phase of our neural network. Next, cysteine oxidation state is predicted, then each pair of cysteines in the protein sequence is assigned a likelihood of forming a disulfide bond—this is performed by means of a novel architecture (diresidue neural network). Finally, Rothberg's implementation of Gabow's maximum weighted matching algorithm is applied to diresidue neural network scores in order to produce the final connectivity prediction. Our novel neural network-based approach achieves results that are comparable and in some cases better than the current state-of-the-art methods.

On the Perception of Molecules from 3D Atomic Coordinates

A method is presented for perceiving chemical types of atoms in molecules given 3D atomic coordinates and element identities. The method assigns hybridizations, bond orders, and formal charges for structures whether hydrogen atoms are present. The Maximum Weighted Matching algorithm for nonbipartite graphs is used to assign bond orders with weights derived from statistics of a large collection of organic molecules. Results form tests on a collection of functional groups, heterocycles, entries from the Protein Data Bank, and Cambridge Structural Database as well as a comparison to other methods, are presented and discussed.

Packet scheduling in input-queued switches with a speedup of less than two and scheduling algorithms for switches with a configuration overhead

Input-queued switches and the solution of input/output contention by scheduling algorithms have been widely investigated. Most research has focused on switches for fixed-size packets. This contrasts with the variable size packets of IP networks. Previous research on fixed packet length has only focused on maximum weight matching algorithms. As maximum weight matching algorithms are computationally very complex, it is of interest to investigate less complex, but stable algorithms that take into account the variable packet size of data packets. In this paper, we investigate how the class of maximal matching algorithms deployed in switches with a speedup of less than two can be modified to take into account the varying packet sizes. Using a novel model for the dynamics of maximal matching algorithms, we show that modified maximal matching algorithms guarantee stability of the switch and establish bounds on the average delay experienced by a packet. In the second part of the paper, we apply the techniques developed for networks with variable packet size to the design of a scheduling algorithm for switches with large configuration overhead. We design a maximal weight matching algorithm for a switch with configuration overhead and determine the minimum speedup required to guarantee the stability of the switch.

Distributed scheduling policies in networks of input-queued packet switches

Scheduling algorithms for input-queued packet switches have been widely researched. It has been shown that various classes of scheduling algorithms provide guarantees on stability and on average delay for single switches. However, recent research has demonstrated that most of these scheduling algorithms do not guarantee stability for networks of switches. Most of the research that treats networks of switches proposes switching policies that require coordination among the single switches. The problem to find <i>distributed</i> scheduling policies that guarantee the stability of a network of switches has so far only been investigated for a policy based on a computationally very complex maximum weight matching algorithm. In this paper, we investigate <i>distributed</i> scheduling algorithms of <i>low complexity</i> that belong to the classes of maximal weight matching algorithms, <i>p</i>-maximal weight matching algorithms for switch architectures based on a space-division multiplexing extension, and MNCM algorithms. For these scheduling algorithms, we prove the stability of networks of input-queued switches where all switches deploy the same scheduling policy. We also show that networks of input-queued switches in which specific classes of different switching policies are deployed simultaneously at different switches are stable.

Prediction of consensus RNA secondary structures including pseudoknots

Most functional RNA molecules have characteristic structures that are highly conserved in evolution. Many of them contain pseudoknots. Here, we present a method for computing the consensus structures including pseudoknots based on alignments of a few sequences. The algorithm combines thermodynamic and covariation information to assign scores to all possible base pairs, the base pairs are chosen with the help of the maximum weighted matching algorithm. We applied our algorithm to a number of different types of RNA known to contain pseudoknots. All pseudoknots were predicted correctly and more than 85 percent of the base pairs were identified.

Bounds on delays and queue lengths in input-queued cell switches

In this article, we develop a general methodology, mainly based upon Lyapunov functions, to derive bounds on average delays, and on averages and variances of queue lengths in complex systems of queues. We apply this methodology to cell-based switches and routers, considering first output-queued (OQ) architectures, in order to provide a simple example of our methodology, and then both input-queued (IQ), and combined input/output queued (CIOQ) architectures. These latter switching architectures require a scheduling algorithm to select at each slot a subset of input-buffered cells that can be transferred toward output ports. Although the stability properties (i.e., the limit throughput) of IQ and CIOQ cell-based switches were already studied for several classes of scheduling algorithms, very few analytical results concerning cell delays or queue lengths are available in the technical literature. We concentrate on Maximum Weight Matching (MWM) and Maximal Size Matching (mSM) scheduling algorithms; while the former was proved to maximize throughput, the latter allows simpler implementation. The derived bounds are shown to be rather tight when compared to simulation results.

Architectural energy optimization by bus splitting

This paper proposes split shared-bus architecture to reduce the energy dissipation for global data exchange among a set of interconnected modules. The bus splitting problem for minimum energy is formulated as a minimum-exchange bus split problem, which is shown to be NP-complete. The problem is solved heuristically by using a maximum-weight matching algorithm and combinatorial search. Experimental results show that the energy saving of split-bus architecture compared to monolithic-bus architecture varies from 16% to 50%, depending on the characteristics of the data transfer among the modules and the configuration of the split-bus. The proposed split-bus architecture can be extended to multiway split-bus architecture when large numbers of modules are to be connected.

An implementable parallel scheduler for input-queued switches

The Apsara algorithm is an input-queued switch scheduler that uses limited parallelism to find a matching in a single iteration, as compared to the O(N/sup 3/) iterations of the more common maximum-weight matching algorithm. The Apsara algorithm also achieves a throughput of up to 100 percent and has very good delay properties.

Achieving 100% throughput in an input-queued switch

It is well known that head-of-line blocking limits the throughput of an input-queued switch with first-in-first-out (FIFO) queues. Under certain conditions, the throughput can be shown to be limited to approximately 58.6%. It is also known that if non-FIFO queueing policies are used, the throughput can be increased. However, it has not been previously shown that if a suitable queueing policy and scheduling algorithm are used, then it is possible to achieve 100% throughput for all independent arrival processes. In this paper we prove this to be the case using a simple linear programming argument and quadratic Lyapunov function. In particular, we assume that each input maintains a separate FIFO queue for each output and that the switch is scheduled using a maximum weight bipartite matching algorithm. We introduce two maximum weight matching algorithms: longest queue first (LQF) and oldest cell first (OCF). Both algorithms achieve 100% throughput for all independent arrival processes. LQF favors queues with larger occupancy, ensuring that larger queues will eventually be served. However, we find that LQF can lead to the permanent starvation of short queues. OCF overcomes this limitation by favoring cells with large waiting times.

Approximation algorithms for covering a graph by vertex‐disjoint paths of maximum total weight

AbstractWe consider the problem of covering a weighted graph G = (V, E) by a set of vertex‐disjoint paths, such that the total weight of these paths is maximized. This problem is clearly NP‐complete, since it contains the Hamiltonian path problem as a special case. Three approximation algorithms for this problem are presented, exhibiting a complexity‐performance trade‐off. First, we develop an algorithm for covering undirected graphs. The time complexity of this algorithm is O(|E|log|E|), and its performance‐ratio is ½. Second, we present an algorithm for covering undirected graphs, whose performance‐ratio is ⅔. This algorithm uses a maximum weight matching algorithm as a subroutine, which dominates the overall complexity of our algorithm. Finally, we develop an algorithm for covering directed graphs, whose performanceratio is ⅔. This algorithm uses a maximum weight bipartite matching algorithm as a subroutine, which dominates the overall complexity of the algorithm.

Improvement and realization for the maximum weight matching algorithm

Some new concepts of effective incidence matrix, ascending order adjacency matrix and end-result vertex are introduced, and some improvements of the maximum weight matching algorithm are made. With this method a computer program in FORTRAN language is realized on the computers FELIX C-512 and IBM-PC. Good results are obtained in practical operations.

A note on efficient SS/TDMA assignment algorithms

A time-slot assignment procedure using the maximum-weight matching algorithm is proposed and investigated. In contrast with previous methods, based on the maximum-cardinality matching, the proposed procedure allows the inclusion of known heuristics in a more direct manner. Computer simulation gives evidence of efficiency improvements by using this approach. >