Fair-by-design matching

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.

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.

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.

For a graph G=(V,E), finding a set of disjoint edges that do not share any vertices is called a matching problem, and finding the maximum matching is a fundamental problem in the theory of distributed graph algorithms. Although local algorithms for the approximate maximum matching problem have been widely studied, exact algorithms has not been much studied. In fact, no exact maximum matching algorithm that is faster than the trivial upper bound of O(n^2) rounds is known for the general instance. In this paper, we propose a randomized O(s_{max}^{3/2}+log n)-round algorithm in the CONGEST model, where s_{\max} is the size of maximum matching. This is the first exact maximum matching algorithm in o(n^2) rounds for general instances in the CONGEST model. The key technical ingredient of our result is a distributed algorithms of finding an augmenting path in O(s_{\max}) rounds, which is based on a novel technique of constructing a sparse certificate of augmenting paths, which is a subgraph of the input graph preserving at least one augmenting path. To establish a highly parallel construction of sparse certificates, we also propose a new characterization of sparse certificates, which might also be of independent interest.

ABSTRACTI introduce a new graph‐theoretic property called abundant neighborhoods. This property is motivated by studying the thickness of economic markets. A vertex is, roughly, guaranteed to match if and only if it has an abundant neighborhood. This fact holds across numerous variants of two‐sided markets that are studied across the economics, operations research, and computer science literature. I introduce a new formalism to study these variants under a unifying framework, which I call matching rules, allowing us to study hitherto different types of markets (equivalently, graph matching problems) together. In particular, stable matchings, max‐weight matchings, and rank‐maximal matchings can be studied together as they are all surjective maximal matching rules. Lastly, the abundant neighborhood property can be used to study properties of maximal matchings: a vertex is matched in all maximal matchings if and only if it has an abundant neighborhood. With this observation, I develop a novel decomposition for studying maximal matchings. I use it to introduce a new integer programming formulation of the minimum maximal matching problem, which represents the worst‐case performance of a market. I show with experiments that using this formulation solves the problem for dense graphs with up to 500 vertices with 30%–50% less time than previous approaches from the literature and yields much tighter solutions for timed‐out instances.

Matching and packing problems have formed an important class of NP-hard problems. There have been a number of recently developed techniques for parameterized algorithms for these problems, including greedy localization, color-coding plus dynamic programming, and randomized divide-and-conquer. In this paper, we provide further theoretical study on the structures of these problems, and develop improved algorithmic methods that combine existing and new techniques to obtain improved algorithms for matching and packing problems. For the 3-set packing problem, we present a deterministic algorithm of time O *(4.613k), which significantly improves the previous best deterministic algorithm of time O *(12.83k). For the 3-d matching problem, we develop a new randomized algorithm of running time O *(2.323k) and a new deterministic algorithm of running time O *(2.773k). Our randomized algorithm improves the previous best randomized algorithm of running time O *(2.523k), and our deterministic algorithm significantly improves the previous best deterministic algorithm of running time O *(12.83k). Our results also imply improved algorithms for various triangle packing problems in graphs.KeywordsTime ComplexityDynamic ProgrammingMatch ProblemPacking ProblemDynamic Programming AlgorithmThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper, we consider the following distributed bipartite matching problems: Let G=(L, R; E) be a bipartite graph in which boys are part L (left nodes), and girls are part R (right nodes.) There is an edge (li, rj) ∈ E iff boy li is interested in girl rj. Every boy li will propose to a girl rj among all those he is interested in, i.e., his adjacent right nodes in the bipartite graph G. If several boys propose to the same girl, only one of them will be accepted by the girl. We assume that none of the boys communicate with others. This matching problem is typical of distributed computing under incomplete information: Each boy only knows his own preference but none of the others. We first study the one-round matching problem: each boy proposes to at most one girl, so that the total number of girls receiving a proposal is maximized. If the maximum matching is M, then no deterministic algorithm can produce a matching of size not bounded by a constant, but a randomized algorithm achieves √M—and this is shown optimal by an adversary argument. If we allow many rounds in matching, with the senders learning from their failures, then the ratio is unbounded when the number of rounds is smaller than Δ, and becomes bounded (two) at the Δ-th round. In contrast, an extension of the one-round randomized algorithm establishes that there is no such discontinuity in the randomized case. This randomized result is also matched by an upper bound of asymptotically the same order.

In this paper, we deal with both the complexity and the approximability of the labeled perfect matching problem in bipartite graphs. Given a simple graph G = (V,E) with n vertices with a color (or label) function L : E→ {c1,...,cq}, the labeled maximum matching problem consists in finding a maximum matching on G that uses a minimum or a maximum number of colors.

Matchability and [formula omitted]-maximal matchings

For a combined input and output queued (CIOQ) switch, maximal matching (MM) algorithm with a speedup of 2 has been known to deliver 100% throughput under any admissible traffic, where in each time slot, two independent schedulings and two cell transferrings are made respectively. This paper proposes a new kind of extended maximal matching (EMM) algorithm, which just utilizes a little information of VOQ length. We show that the implementation complexity of CIOQ switches is reduced by using the EMM(2) algorithm, where only one scheduling and two cell transferrings (data speedup of 2) are necessary in each time slot to achieve 100% throughput when input traffic is admissible. The EMM(2) algorithm can be easily realized by modifying the existing MM algorithms. In this paper, we provide a practical instance of EMM(2) algorithm, named EiSLIP(1,2), based on the well-known iSLIP algorithm. Simulations show that EiSLIP(1,2) algorithm with a data speedup of 2 achieves almost the same delay performance as output queued policy under uniform and non-uniform traffic with Bernoulli arrival, as well as the bursty traffic.

We study the Maximum Cardinality Matching (MCM) and the Maximum Weight Matching (MWM) problems, on trees and on some special classes of graphs, in the Online Preemptive and the Incremental Dynamic Graph models. In the Online Preemptive model, the edges of a graph are revealed one by one and the algorithm is required to always maintain a valid matching. On seeing an edge, the algorithm has to either accept or reject the edge. If accepted, then the adjacent edges are discarded, and all rejections are permanent. In this model, the complexity of the problems is settled for deterministic algorithms [11, 15]. Epstein et al. [5] gave a 5.356-competitive randomized algorithm for MWM, and also proved a lower bound of 1.693 for MCM. The same lower bound applies for MWM.

In the process of informatization, there are also some new problems, mainly information can’t be shared and integrated, distributed resources can’t be used effectively, these problems make the industry face new challenges. The goal of this paper is to combine the grid technology and ontology organically, to build a unified information system integration and interoperation platform based on semantics, to realize information sharing and accelerate the pace of informatization. The method is to construct the whole structure of the system according to the actual needs of the system. This paper firstly analyzes the current research status and existing problems of semantic grid service matching, and proposes a semantic layered matching algorithm based on Massimo Paolucci elastic matching algorithm. To verify the feasibility and effectiveness of the hierarchical matching algorithm based on semantics, a prototype system named SGSM was designed and its functional model, matching process and performance were studied. Experimental results show that for the semantic-based hierarchical matching algorithm proposed in this paper, the threshold value of service semantic correlation degree is 0.84, the threshold value of service basic concept matching degree is 0.89, the threshold value of service comprehensive similarity degree is 0.66, and the threshold value of service quality matching degree is 0.78. Statistics through the experiment, the above three methods of recall, respectively, 33%, 62%, 85%, the precision is respectively: 29%, 57%, 88%, and illustrate the hierarchical matching algorithm based on semantic is feasible in practical application, compared with the traditional service based on keyword matching algorithm and Massimo Paolucci elastic matching algorithm on the recall and precision are improved significantly.

Gravity aided inertial navigation system (GAINS), which uses earth gravitational anomaly field for navigation, holds strong potential as an underwater navigation system. The gravity matching algorithm is one of the key factors in GAINS. Existing matching algorithms cannot guarantee the matching accuracy in the matching algorithms based gravity aided navigation when the initial errors are large. Evolutionary algorithms, which are mostly have the ability of global optimality and fast convergence, can be used to solve the gravity matching problem under large initial errors. However, simply applying evolutionary algorithms to GAINS may lead to false matching. Therefore, in order to deal with the underwater gravity matching problem, it is necessary to improve the traditional evolutionary algorithms. In this paper, an affine transformation based artificial bee colony (ABC) algorithm, which can greatly improve the positioning precision under large initial errors condition, is developed. The proposed algorithm introduces affine transformation to both initialization process and evolutionary process of ABC algorithm. The single-point matching strategy is replaced by the strategy of matching a sequence of several consecutive position vectors. In addition, several constraints are introduced to the process of evolution by using the output characteristics of the inertial navigation system (INS). Simulations based on the actual gravity anomaly base map have been performed for the validation of the proposed algorithm.

Maximum matchings in general graphs through randomization

Port partitioning and dynamic queueing for IP forwarding