Maximum Weight Matching Research Articles

Double-Auction-Based Optimal User Assignment for Multisource–Multirelay Cellular Networks

Recently, as it can greatly increase the capacity of cellular networks through spatial diversity, cooperative communications has been obtaining more and more attention. As a widely used schema, user (user equipment, UE) cooperation presents its advantage. However, due to the users' selfish nature, UE may be unwilling to serve as a relay node if they cannot obtain a corresponding reward. On the contrary, to save energy for longer standby time, particularly when there is energy shortage, many source users would like to purchase the relay service from other idle UE. Therefore, reconciling the demand of both sides is a challenging problem to be resolved. In this paper, a realistic double-auction scenario is constructed between multiple source UE and multiple idle UE in a cellular network. We take the avaricious psychology of network entities into consideration by determining the ask and bid prices through a markup, which is the function of their residual energy. To solve this double-auction-based optimal relay assignment problem, we transform it into maximum matching (MM) and maximum weighted matching (MWM) problems, respectively, and we solve them by corresponding algorithms. Experimental results show that the proposed algorithms dramatically maximize the system performance involving successful source–relay pairs, system throughput, and social welfare (SW), compared with other idealized truthful double-auction scheme that only consider the system throughput.

Domain similarity based orthology detection

BackgroundOrthologous protein detection software mostly uses pairwise comparisons of amino-acid sequences to assert whether two proteins are orthologous or not. Accordingly, when the number of sequences for comparison increases, the number of comparisons to compute grows in a quadratic order. A current challenge of bioinformatic research, especially when taking into account the increasing number of sequenced organisms available, is to make this ever-growing number of comparisons computationally feasible in a reasonable amount of time. We propose to speed up the detection of orthologous proteins by using strings of domains to characterize the proteins.ResultsWe present two new protein similarity measures, a cosine and a maximal weight matching score based on domain content similarity, and new software, named porthoDom. The qualities of the cosine and the maximal weight matching similarity measures are compared against curated datasets. The measures show that domain content similarities are able to correctly group proteins into their families. Accordingly, the cosine similarity measure is used inside porthoDom, the wrapper developed for proteinortho. porthoDom makes use of domain content similarity measures to group proteins together before searching for orthologs. By using domains instead of amino acid sequences, the reduction of the search space decreases the computational complexity of an all-against-all sequence comparison.ConclusionWe demonstrate that representing and comparing proteins as strings of discrete domains, i.e. as a concatenation of their unique identifiers, allows a drastic simplification of search space. porthoDom has the advantage of speeding up orthology detection while maintaining a degree of accuracy similar to proteinortho. The implementation of porthoDom is released using python and C++ languages and is available under the GNU GPL licence 3 at http://www.bornberglab.org/pages/porthoda.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0570-8) contains supplementary material, which is available to authorized users.

ScaffMatch: scaffolding algorithm based on maximum weight matching.

Next-generation high-throughput sequencing has become a state-of-the-art technique in genome assembly. Scaffolding is one of the main stages of the assembly pipeline. During this stage, contigs assembled from the paired-end reads are merged into bigger chains called scaffolds. Because of a high level of statistical noise, chimeric reads, and genome repeats the problem of scaffolding is a challenging task. Current scaffolding software packages widely vary in their quality and are highly dependent on the read data quality and genome complexity. There are no clear winners and multiple opportunities for further improvements of the tools still exist. This article presents an efficient scaffolding algorithm ScaffMatch that is able to handle reads with both short (<600 bp) and long (>35 000 bp) insert sizes producing high-quality scaffolds. We evaluate our scaffolding tool with the F score and other metrics (N50, corrected N50) on eight datasets comparing it with the most available packages. Our experiments show that ScaffMatch is the tool of preference for the most datasets. The source code is available at http://alan.cs.gsu.edu/NGS/?q=content/scaffmatch. mandric@cs.gsu.edu Supplementary data are available at Bioinformatics online.

Temporal Flexibility Revisited: Maximizing Flexibility by Computing Bipartite Matchings

We discuss two flexibility metrics for Simple Temporal Networks (STNs): the so-called naive flexibility metric based on the difference between earliest and latest starting times of temporal variables, and a recently proposed concurrent flexibility metric. We establish an interesting connection between the computation of these flexibility metrics and properties of the minimal distance matrix DS of an STN S: the concurrent flexibility metric can be computed by finding a minimum weight matching of a weighted bipartite graph completely specified by DS, while the naive flexibility metric corresponds to computing a maximum weight matching in the same graph. From a practical point of view this correspondence offers an advantage: instead of using an O(n5) LP-based approach, reducing the problem to a matching problem we derive an O(n3) algorithm for computing the concurrent flexibility metric.

Submodular maximization meets streaming: matchings, matroids, and more

We study the problem of finding a maximum matching in a graph given by an input stream listing its edges in some arbitrary order, where the quantity to be maximized is given by a monotone submodular function on subsets of edges. This problem, which we call maximum submodular-function matching (MSM), is a natural generalization of maximum weight matching (MWM), which is in turn a generalization of maximum cardinality matching. We give two incomparable algorithms for this problem with space usage falling in the semi-streaming range--they store only $$O(n)$$O(n) edges, using $$O(n\log n)$$O(nlogn) working memory--that achieve approximation ratios of 7.75 in a single pass and $$(3+\varepsilon )$$(3+?) in $$O(\varepsilon ^{-3})$$O(?-3) passes respectively. The operations of these algorithms mimic those of Zelke's and McGregor's respective algorithms for MWM; the novelty lies in the analysis for the MSM setting. In fact we identify a general framework for MWM algorithms that allows this kind of adaptation to the broader setting of MSM. Our framework is not specific to matchings. Rather, we identify a general pattern for algorithms that maximize linear weight functions over and prove that such algorithms can be adapted to maximize a submodular function. The notion of independence here is very general; in particular, appealing to known weight-maximization algorithms, we obtain results for submodular maximization over hypermatchings in hypergraphs as well as independent sets in the intersection of multiple matroids.

A QOS Based Load Balanced Switch

The simple architecture with high forwarding capacity bandwidth is load balancing switch is build with two stage switch fabric to eliminate the mis sequencing problems and kept packets of the same flow in the order of load balanced two stage switch. Before load balancing two stages has perform with the Full frame first algorithm and use centralized scheduler to eliminate those mis sequencing problemsand getting the 100% throughput result. There comes at some additional cost and needs costly online scheduling algorithms and need for a complex scheduler and quality being reduced. In this paper we introduce the two stage switch fabric with round robin scheduling algorithmis used to solve mis sequencing problems and two maximum weight matching algorithms Longest queue first(LQF) and Oldest cell first(OCF) to achieve 100% throughput results. Theoretical analysis and simulation results shows that using these algorithms, achieve all the possible outcome results in the switch. � The simple architecture with the load balancing scheme perform with interesting two different stage switch fabric to eliminate the mis sequencing problems and kept packets of the same flow to the destination path in the order of load balanced two stage switch fabric. The two stage load balancing switch is more scalable than the any other switch in the network architecture. Hardly load balanced switch got some problem with that, on sending and receiving the data in wired or wireless networks(8), the major problem with that is mis sequencing problems has arised to loss of data packets or mis matched data formats. Somehow in earlier they are tired to clear those problems with the algorithms named, Full frame first algorithm to get mis sequencing problems and they put the centralized schedular to achieve the 100% throughput results(4)(2) in their data packets.Oftenly they got the perfect data packets arrival in destination, but the problem with that methodology is the quality of data is reduced to lower. And manually they they need costly online scheduling algorithms to rectify the mis matching of data and need more complex schedular to achieve the 100% throughput result of outcome data. We introduce in this paper to rectify the mis sequencing problems(1) and avoid the costly online scheduling algorithms, we use Round robin scheduling algorithms(RRS) to rectify the mis matching of data packets in the tcp applications and two maximum weight matching algorithms namely, Longest queue first(LOQ) and Oldest cell first(OCF) to achieve 100% throughput result for all independent arrival packets.(11)These algorithms are used to eliminate the complex schedular and needs of online costly scheduling algorithm to schedule the data packets in the destination node. The another approach of this proposed is to get the high quality of data packets in destination node which is the data which is send by sender, the receiver also got the same quality of data(9) without defragmentation and reduction of quality. We observed that in the algorithms and methodolgy of using those above like, RRS, LOQ and OCF, not only to solve mis sequencing problems and also get quality of data packets service of the same aaplication(10). Yet we are consider more algorithm to get the quality of data packets. Our idea is to just keep packets

Bayesian incentive compatibility via matchings

Optimally allocating cellphone spectrum, advertisements on the Internet, and landing slots at airports is computationally intractable. When the participants may strategize, not only must the optimizer deal with complex feasibility constraints but also with complex incentive constraints. We give a very simple method for constructing a Bayesian incentive compatible mechanism from any, potentially non-optimal, algorithm that maps agents' reports to an allocation. The expected welfare of the mechanism is, approximately, at least that of the algorithm on the agents' true preferences.The construction is based on a maximum weight matching in the type space of each agent that be calculated quickly when the type spaces are reasonably sized. Furthermore, the computation can be performed independently for each agent and, therefore, scales well with the number of agents. A similar construction was previously given by Hartline and Lucier (2010) for agents with single-dimensional types; ours allows multi-dimensional types.

The cost of perfection for matchings in graphs

Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. Motivated by the computer graphics application in triangle meshes, where we seek to convert a triangulation into a quadrangulation by merging pairs of adjacent triangles, we focus mainly on bridgeless cubic graphs.First, we characterize graphs that attain the extreme ratios. Second, we present a lower bound for all bridgeless cubic graphs. Third, we present upper bounds for subclasses of bridgeless cubic graphs, most of which are shown to be tight. Additionally, we present tight bounds for the class of regular bipartite graphs.

Online Algorithms for Basestation Allocation

Design of online algorithms for assigning mobile users to basestations is considered with the objective of maximizing the sum-rate, when all users associated to any one basestation equally share each basestation's resources. Each user on its arrival reveals the rates it can obtain if connected to each of the basestations, and the problem is to assign each user to any one basestation irrevocably and without delay so that the sum-rate is maximized at the end of all user arrivals. In online algorithms, at each user arrival, the rates of future users are assumed to be unknown, and no assumptions are made about their statistics. Online algorithms with constant factor loss in comparison to offline algorithms (that know both the user arrival and user rates profile in advance) are derived. The proposed online algorithms are motivated from the famous online k-secretary problem and online maximum weight matching problem.

Risk-Aware Cooperative Spectrum Access for Multi-Channel Cognitive Radio Networks

In this paper, risk-aware cooperative spectrum access schemes for cognitive radio networks (CRNs) with multiple channels are proposed, whereby multiple primary users (PUs) operating over different channels choose trustworthy secondary users (SUs) as relays to improve throughput, and in return SUs gain transmission opportunities. To study the multi-channel cooperative spectrum access, cooperation over single channel is investigated first, which involves a PU selecting the suitable SU and granting a period of access time to the selected SU as a reward, considering trustworthiness of SUs. The above procedure is modeled as a Stackelberg game, through which access time allocation and power allocation are obtained. Based on the above results, cooperation over multiple channels is studied from the perspectives of the primary network and secondary network, respectively. Two schemes are proposed accordingly: the primary network-centric matching (PCM) scheme and the secondary network-centric cluster-based (SCC) scheme. In PCM scheme, cooperating SU for each channel is determined to maximize the total utility of the primary network, which is formulated as a maximum weight matching problem. In SCC scheme, SUs first form a cluster to share the channel state information (CSI), and the best SUs are selected for cooperation with PUs over different channels to obtain the maximum aggregate access time for the secondary network. Then, SUs share the obtained resource using congestion game and quadrature signalling. Numerical results demonstrate that, with the proposed schemes, PUs can achieve higher throughput, while SUs can obtain longer average access time, compared with the random channel access approach.

Linear-Time Approximation for Maximum Weight Matching

The maximum cardinality and maximum weight matching problems can be solved in Õ ( m √ n ) time, a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article, we demonstrate that this “ m √ n barrier” can be bypassed by approximation. For any ε &gt; 0, we give an algorithm that computes a (1 − ε )-approximate maximum weight matching in O ( mε −1 log ε −1 ) time, that is, optimal linear time for any fixed ε . Our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error.

Optimal Matching Forests and Valuated Delta-Matroids

The matching forest problem in mixed graphs is a common generalization of the matching problem in undirected graphs and the branching problem in directed graphs. Giles presented an $\mathrm{O}(n^{2}m)$-time algorithm for finding a maximum-weight matching forest, where $n$ is the number of vertices and $m$ is that of edges, and a linear system describing the matching forest polytope. Later, Schrijver proved total dual integrality of the linear system. In the present paper, we reveal another nice property of matching forests: the degree sequences of the matching forests in any mixed graph form a delta-matroid, and the weighted matching forests induce a valuated delta-matroid. We remark that the delta-matroid is not necessarily even, and the valuated delta-matroid induced by weighted matching forests slightly generalizes the well-known notion of Dress and Wenzel's valuated delta-matroids. By focusing on the delta-matroid structure and reviewing Giles' algorithm, we design a simpler $\mathrm{O}(n^{2}m)$-time ...

On the Stability Region of Maximum Weighted Matching Server Allocation Policy

In this paper, we study the stability region of a multi-server queueing system for which Maximum Weighted Matching (MWM) server allocation policy is known to be throughput-optimal. We derive a linear algebraic characterization of the system stability region polytope (or equivalently MWM stability region) by means of a finite set of linear inequalities. Such a characterization of the stability region is useful for solving network stochastic optimization problems and also evaluating the performance of MWM server allocation policy, e.g., deriving explicit performance bounds for the average queueing delay and flow measurement metrics. Furthermore, using the linear algebraic form of the stability region, we derive an upper bound for the average queueing delay of MWM policy.

Ancient eudicot hexaploidy meets ancestral eurosid gene order.

BackgroundA hexaploidization event over 125 Mya underlies the evolutionary lineage of the majority of flowering plants, including very many species of agricultural importance. Half of these belong to the rosid subgrouping, containing severals whose genome sequences have been published. Although most duplicate and triplicate genes have been lost in all descendants, clear traces of the original chromosome triples can be discerned, their internal contiguity highly conserved in some genomes and very fragmented in others. To understand the particular evolutionary patterns of plant genomes, there is a need to systematically survey the fate of the subgenomes of polyploids, including the retention of a small proportion of the duplicate and triplicate genes and the reconstruction of putative ancestral intermediates between the original hexaploid and modern species, in this case the ancestor of the eurosid clade.ResultsWe quantitatively trace the fate of gene triples originating in the hexaploidy across seven core eudicot flowering plants, and fit this to a two-stage model, pre- and post-radiation. We also measure the simultaneous dynamics of duplicate orthologous gene loss in three rosids, as influenced by biological functional class. We propose a new protocol for reconstructing ancestral gene order using only gene adjacency data from pairwise genomic analyses, based on repeating MAXIMUM WEIGHT MATCHING at two levels of resolution, an approach designed to transcend limitations on reconstructed contig size, while still avoiding the ambiguities of a multiplicity of solutions. Applied to three high-quality rosid genomes without subsequent polyploidy events, our automated procedure reconstructs the ancestor of the eurosid clade.ConclusionsThe gene loss analysis and the ancestor reconstruction present complementary assessments of post-hexaploidization evolution, the first at the level of individual gene families within and across sister genomes and the second at the chromosome level. Despite the loss of more than 95% of gene duplicates and triplicates, and despite major structural rearrangement, our reconstructed eurosid ancestor clearly identifies the three regions corresponding to each of the seven original chromosomes of the earlier pre-hexaploid ancestor. Functional analysis confirmed trends reported for more recent plant polyploidy events: genes involved with regulation and responses were retained in multiple copies, while genes involved with metabolic processes were lost.

A reduction algorithm for the weighted stable set problem in claw-free graphs

In this article the Lovász–Plummer clique reduction is extended to the weighted case and used to find a maximum weight stable set in a claw-free graph G with n nodes in O(n2(n2+L(n))) time, where L(n) is the complexity of finding a maximum weight augmenting path in a line graph H with n nodes. The best algorithm known to date to solve the latter problem is Gabow’s maximum weight matching algorithm (applied to the root graph of H) which has a complexity of O(n2logn). It follows that our algorithm can produce a maximum weight stable set in a claw-free graph in O(n4logn) time.

AN EFFICIENT NC ALGORITHM FOR APPROXIMATE MAXIMUM WEIGHT MATCHING

We present an alternative implementation of the (1 – ϵ) factor NC approximation algorithm for the maximum weight matching by Hougardy et al. [1]. Our implementation, on the EREW PRAM model of computation, achieves an [Formula: see text] factor improvement on both the execution time and the number of processors.

Cell tracking in microscopic video using matching and linking of bipartite graphs

Automated visual tracking of cells from video microscopy has many important biomedical applications. In this paper, we track human monocyte cells in a fluorescent microscopic video using matching and linking of bipartite graphs. Tracking of cells over a pair of frames is modeled as a maximum cardinality minimum weight matching problem for a bipartite graph with a novel cost function. The tracking results are further refined using a rank-based filtering mechanism. Linking of cell trajectories over different frames are achieved through composition of bipartite matches. The proposed solution does not require any explicit motion model, is highly scalable, and, can effectively handle the entry and exit of cells. Our tracking accuracy of (97.97±0.94)% is superior than several existing methods [(95.66±2.39)% [11], (94.42±2.08)% [20], (81.22±5.75)% [13], (78.31±4.70)% [14]] and is highly comparable (98.20±1.22)% to a recently published algorithm [26].

New approaches to multi-objective optimization

A natural way to deal with multiple, partially conflicting objectives is turning all the objectives but one into budget constraints. Many classical optimization problems, such as maximum spanning tree and forest, shortest path, maximum weight (perfect) matching, maximum weight independent set (basis) in a matroid or in the intersection of two matroids, become NP-hard even with one budget constraint. Still, for most of these problems efficient deterministic and randomized approximation schemes are known. Not much is known however about the case of two or more budgets: filling this gap, at least partially, is the main goal of this paper. In more detail, we obtain the following main results: Using iterative rounding for the first time in multi-objective optimization, we obtain multi-criteria PTASs (which slightly violate the budget constraints) for spanning tree, matroid basis, and bipartite matching with $$k=O(1)$$ budget constraints. We present a simple mechanism to transform multi-criteria approximation schemes into pure approximation schemes for problems whose feasible solutions define an independence system. This gives improved algorithms for several problems. In particular, this mechanism can be applied to the above bipartite matching algorithm, hence obtaining a pure PTAS. We show that points in low-dimensional faces of any matroid polytope are almost integral, an interesting result on its own. This gives a deterministic approximation scheme for $$k$$ -budgeted matroid independent set. We present a deterministic approximation scheme for $$k$$ -budgeted matching (in general graphs), where $$k=O(1)$$ . Interestingly, to show that our procedure works, we rely on a non-constructive result by Stromquist and Woodall, which is based on the Ham Sandwich Theorem.

A combinatorial approach to the peptide feature matching problem for label-free quantification

Label-free quantification is an important approach to identify biomarkers, as it measures the quantity change of peptides across different biological samples. One of the fundamental steps for label-free quantification is to match the peptide features that are detected in two datasets to each other. Although ad hoc software tools exist for the feature matching, the definition of a combinatorial model for this problem is still not available. A combinatorial model is proposed in this article. Each peptide feature contains a mass value and a retention time value, which are used to calculate a matching weight between a pair of features. The feature matching is to find the maximum-weighted matching between the two sets of features, after applying a to-be-computed time alignment function to all the retention time values of one set of the features. This is similar to the maximum matching problem in a bipartite graph. But we show that the requirement of time alignment makes the problem NP-hard. Practical algorithms are also provided. Experiments on real data show that the algorithm compares favorably with other existing methods. binma@uwaterloo.ca Supplementary data are available at Bioinformatics online.

A Graph-Based Cooperative Scheduling Scheme for Vehicular Networks

Vehicle-to-vehicle (V2V) communications are considered to be a significant step forward toward a highly secure and efficient intelligent transportation system. In this paper, we propose the use of graph theory to formulate the problem of cooperative communications scheduling in vehicular networks. In lieu of exhaustive search with intractable complexity for the maximum sum rate (MSR), we propose a bipartite-graph-based (BG) scheduling scheme to allocate the vehicle-to-infrastructure (V2I) and V2V links for both single-hop and dual-hop communications. The Kuhn–Munkres (KM) algorithm is adopted to solve the problem of maximum weighted matching (MWM) of the constructed BG. Simulation results indicate that the proposed scheme performs extremely close to the optimal scheme and results in better fairness among vehicle users with considerably lower computational complexity. Moreover, cooperative communications can improve both the throughput and spectral efficiency (SE) of vehicular networks.