Maximum Matching Research Articles

MONI: A Pangenomic Index for Finding Maximal Exact Matches.

Recently, Gagie et al. proposed a version of the FM-index, called the r-index, that can store thousands of human genomes on a commodity computer. Then Kuhnle et al. showed how to build the r-index efficiently via a technique called prefix-free parsing (PFP) and demonstrated its effectiveness for exact pattern matching. Exact pattern matching can be leveraged to support approximate pattern matching, but the r-index itself cannot support efficiently popular and important queries such as finding maximal exact matches (MEMs). To address this shortcoming, Bannai et al. introduced the concept of thresholds, and showed that storing them together with the r-index enables efficient MEM finding-but they did not say how to find those thresholds. We present a novel algorithm that applies PFP to build the r-index and find the thresholds simultaneously and in linear time and space with respect to the size of the prefix-free parse. Our implementation called can rapidly find MEMs between reads and large-sequence collections of highly repetitive sequences. Compared with other read aligners-PuffAligner, Bowtie2, BWA-MEM, and CHIC- MONI used 2-11 times less memory and was 2-32 times faster for index construction. Moreover, MONI was less than one thousandth the size of competing indexes for large collections of human chromosomes. Thus, MONI represents a major advance in our ability to perform MEM finding against very large collections of related references.

Finding Maximal Exact Matches Using the r-Index.

Efficiently finding maximal exact matches (MEMs) between a sequence read and a database of genomes is a key first step in read alignment. But until recently, it was unknown how to build a data structure in [Formula: see text] space that supports efficient MEM finding, where r is the number of runs in the Burrows-Wheeler Transform. In 2021, Rossi et al. showed how to build a small auxiliary data structure called thresholds in addition to the r-index in [Formula: see text] space. This addition enables efficient MEM finding using the r-index. In this article, we present the tool that implements this solution, which we call MONI. Namely, we give a high-level view of the main components of the data structure and show how the source code can be downloaded, compiled, and used to find MEMs between a set of sequence reads and a set of genomes.

Global forcing number for maximal matchings in corona products

A global forcing set for maximal matchings of a graph \(G=(V(G), E(G))\) is a set \(S \subseteq E(G)\) such that \(M_1\cap S \ne M_2 \cap S\) for each pair of maximal matchings \(M_1\) and \(M_2\) of G. The smallest such set is called a minimum global forcing set, its size being the global forcing number for maximal matchings \(\phi _{gm}(G)\) of G. In this paper, we establish lower and upper bounds on the forcing number for maximal matchings of the corona product of graphs. We also introduce an integer linear programming model for computing the forcing number for maximal matchings of graphs.

Linear-Time Algorithms for Maximum-Weight Induced Matchings and Minimum Chain Covers in Convex Bipartite Graphs

A bipartite graph G=(U,V,E) is convex if the vertices in V can be linearly ordered such that for each vertex uin U, the neighbors of u are consecutive in the ordering of V. An induced matchingH of G is a matching for which no edge of E connects endpoints of two different edges of H. We show that in a convex bipartite graph with n vertices and mweighted edges, an induced matching of maximum total weight can be computed in O(n+m) time. An unweighted convex bipartite graph has a representation of size O(n) that records for each vertex uin U the first and last neighbor in the ordering of V. Given such a compact representation, we compute an induced matching of maximum cardinality in O(n) time. In convex bipartite graphs, maximum-cardinality induced matchings are dual to minimum chain covers. A chain cover is a covering of the edge set by chain subgraphs, that is, subgraphs that do not contain induced matchings of more than one edge. Given a compact representation, we compute a representation of a minimum chain cover in O(n) time. If no compact representation is given, the cover can be computed in O(n+m) time. All of our algorithms achieve optimal linear running time for the respective problem and model, and they improve and generalize the previous results in several ways: The best algorithms for the unweighted problem versions had a running time of O(n^2) (Brandstädt et al. in Theor. Comput. Sci. 381(1–3):260–265, 2007. https://doi.org/10.1016/j.tcs.2007.04.006). The weighted case has not been considered before.

Energy-Efficient Scheduling for a Cognitive IoT-Based Early Warning System

Flash floods are deemed the most fatal and disastrous natural hazards globally due to their prompt onset that requires a short prime time for emergency response. Cognitive Internet of things (CIoT) technologies including inherent characteristics of cognitive radio (CR) are potential candidates to develop a monitoring and early warning system (MEWS) that helps in efficiently utilizing the short response time to save lives during flash floods. However, most CIoT devices are battery-limited and thus, it reduces the lifetime of the MEWS. To tackle these problems, we propose a CIoT-based MEWS to slash the fatalities of flash floods. To extend the lifetime of the MEWS by conserving the limited battery energy of CIoT sensors, we formulate a resource assignment problem for maximizing energy efficiency. To solve the problem, at first, we devise a polynomial-time heuristic energy-efficient scheduler (EES-1). However, its performance can be unsatisfactory since it requires an exhaustive search to find local optimum values without consideration of the overall network energy efficiency. To enhance the energy efficiency of the proposed EES-1 scheme, we additionally formulate an optimization problem based on a maximum weight matching bipartite graph. Then, we additionally propose a Hungarian algorithm-based energy-efficient scheduler (EES-2), solvable in polynomial time. The simulation results show that the proposed EES-2 scheme achieves considerably high energy efficiency in the CIoT-based MEWS, leading to the extended lifetime of the MEWS without loss of throughput performance.

A generalized ride-matching approach for sustainable shared mobility

On-demand shared mobility is a promising and sustainable transportation approach that can mitigate vehicle externalities, such as traffic congestion and emission. On-demand shared mobility systems require matching of one (one-to-one) or multiple riders (many-to-one) to a vehicle based on real-time information. We propose a novel Graph-based Many-to-One ride-Matching (GMOMatch) algorithm for the dynamic many-to-one matching problem in the presence of traffic congestion. GMOMatch, which is an iterative two-step method, provides high service quality and is efficient in terms of computational complexity. It starts with a one-to-one matching in Step 1 and is followed by solving a maximum weight matching problem in Step 2 to combine the travel requests. To evaluate the performance, it is compared with a ride-matching algorithm developed by Simonetto et al. (2019). Both algorithms are implemented in a micro-traffic simulator to assess their performance and their impact on traffic congestion in Downtown, Toronto road network. In comparison to the Simonetto, GMOMatch improved the service rate, vehicle kilometer traveled and traffic travel time by 32%, 16.07%, and 4%, respectively. The sensitivity analysis indicated that utilizing vehicles with a capacity of 10 can achieve 25% service rate improvement compared to a capacity of 4.

E-Ride: An Adaptive Event-Driven Windowed Matching Framework in Ridesharing

Ridesharing services aim at reducing the users’ travel cost and optimizing the drivers’ routes to satisfy passengers’ expected maximum matching times in practice request dispatching. Existing works can be roughly classified into two types, i.e., online-based and batch-based methods, in which the former mainly focus on responding quickly to the requests and the latter focuses on enumerating request combinations meticulously to improve the service quality. However, online-based methods perform poorly in terms of service quality due to the neglect of the sharing relationship between requests, while batch-based methods fail on efficiency. None of these works can smoothly balance the service quality and matching time cost since the matching window is not sufficiently explored or even neglected. To cope with this problem, we propose a novel framework <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {E}$ </tex-math></inline-formula> -Ride, which comprehensively leverages the matching time window based on the event model. Specifically, an adaptive windowed matching algorithm is proposed to adaptively consider personalized matching time and provide a matching solution with higher service rates at lower latencies. Besides, we maintain the request groups through a mixed graph and further integrate the subsequent arrival requests to optimize the matching results, which can scale to or satisfy online use demands. The extensive experimental results demonstrate the efficiency and effectiveness of our proposed method.

Computing Maximum Matchings in Temporal Graphs

Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the discrete time steps at which $e$ is active. We introduce and study the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking into account the dynamic nature of temporal graphs. In our problem, Maximum Temporal Matching, we are looking for the largest possible number of time-labeled edges (simply time-edges) $(e,t)$ such that no vertex is matched more than once within any time window of $\Delta$ consecutive time slots, where $\Delta \in \mathbb{N}$ is given. The requirement that a vertex cannot be matched twice in any $\Delta$-window models some necessary recovery period that needs to pass for an entity (vertex) after being paired up for some activity with another entity. We prove strong computational hardness results for Maximum Temporal Matching, even for elementary cases. To cope with this computational hardness, we mainly focus on fixed-parameter algorithms with respect to natural parameters, as well as on polynomial-time approximation algorithms.

Methane/CO2 binary gas interaction on some moist, high–volatile bituminous Indian coals: 2. Pure-/mixed-gas adsorption modelling

The pure and mixed methane and CO2 excess experimental adsorption of three moist, high-volatile bituminous Indian coal samples at 40 °C and up to a pressure of ∼6500 kPa, were tested for the applicability of the adsorption models. For pure gas, Langmuir and Dubinin-Astakhov (DA) models were used and it was observed both Langmuir and DA models were matching with experimental data, although the fit with DA model was better. For mixed gas, Extended Langmuir (EL) and Ideal Adsorbed Solutions (IAS) theory were considered for model prediction. Later, the IAS theory was also combined with the Langmuir, DA equation for their applicability on mixed gas modelling. It was observed that none of the models were suitable for predicting the mixed gas adsorption. Although, EL-model show the maximum match for fitting experimental data at lower pressure, the deviation was increased at higher pressures. In general, the experimental CO2 separation factor was observed to decrease with an increase in pressure and CO2 gas concentration. However, the model prediction of CO2 separation factor was only validated by IAS-DA, other models showed inconsistent results.

On a Conjecture about the Saturation Number of Corona Product of Graphs

Let G = (VG, EG) be a simple and connected graph. A set M⊆EG is called a matching if no two edges of M have a common endpoint. A matching M is maximal if it cannot be extended to a larger matching in G. The smallest size of a maximal matching is called the saturation number of G. In this paper, we confirm a conjecture of Alikhani and Soltani about the saturation number of corona product of graphs. We also present the exact value of s(G∘H) where H is a randomly matchable graph.

Double Overt-Leaf Shaped CPW-Fed Four Port UWB MIMO Antenna

This paper presents a 4 × 4 multi-input multi-output antenna array for ultra-wideband applications. The single element of the array is comprised of a modified co-planar waveguide-fed double overt-leaf shaped patch radiator. The co-planar ground is optimized to achieve maximum impedance matching in the operating frequency band. The results show that the single antenna element offers an impedance bandwidth of 13.2 GHz starting from 3.2 GHz to 16.7 GHz. It is also observed from the results that the antenna offers good radiation characteristics and acceptable gain for the frequency band of interest. Furthermore, a 4 × 4 MIMO array is designed by utilizing the polarization diversity technique. To improve the isolation performance among antenna elements, a fan-shaped decoupler is introduced on the other side of the substrate, which ensures minimum isolation of 20 dB. Moreover, the proposed MIMO array operates in the frequency range of 2.75–16.05 GHz. The proposed MIMO array is fabricated and measured for the validation of simulation results, and it is observed that both the results are well in agreement.

A tight bound for shortest augmenting paths on trees

The shortest augmenting path technique is one of the fundamental ideas used in maximum matching and maximum flow algorithms. Since being introduced by Edmonds and Karp in 1972, it has been widely applied in many different settings. Surprisingly, despite this extensive usage, it is still not well understood even in the simplest case: online bipartite matching problem on trees. In this problem a bipartite tree T=(W⊎B,E) is being revealed online, i.e., in each round one vertex from B with its incident edges arrives. It was conjectured by Chaudhuri et al. [6] that the total length of all shortest augmenting paths found is O(nlog⁡n). In this paper we prove a tight O(nlog⁡n) upper bound for the total length of shortest augmenting paths for trees improving over O(nlog2⁡n) bound [3].

An Update-Based Maximum Column Distance Coding Scheme for Index Coding

In this paper, we propose a new scalar linear coding scheme for the index coding problem called update-based maximum column distance (UMCD) coding scheme. The central idea in each transmission is to code messages such that one of the receivers with the minimum size of side information is instantaneously eliminated from unsatisfied receivers. One main contribution of the paper is to prove that the other satisfied receivers can be identified after each transmission, using a polynomial-time algorithm solving the well-known maximum cardinality matching problem in graph theory. This leads to determining the total number of transmissions without knowing the coding coefficients. Once this number and what messages to transmit in each round are found, we then propose a method to determine all coding coefficients from a sufficiently large finite field. We provide concrete instances where the proposed UMCD coding scheme has a better broadcast performance compared to the most efficient existing coding schemes, including the recursive scheme (Arbabjolfaei and Kim, 2014) and the interlinked-cycle cover (ICC) scheme (Thapa <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2017). We prove that the proposed UMCD coding scheme performs at least as well as the MDS coding scheme in terms of broadcast rate. By characterizing two classes of index coding instances, we show that the gap between the broadcast rates of the recursive and ICC schemes and the UMCD scheme grows linearly with the number of messages. Then, we extend the UMCD coding scheme to its vector version by applying it as a basic coding block to solve the subinstances.

Phase transition in the bipartite z-matching

We study numerically the maximum z-matching problems on ensembles of bipartite random graphs. The z-matching problems describes the matching between two types of nodes, users and servers, where each server may serve up to z users at the same time. Using a mapping to standard maximum-cardinality matching, and because for the latter there exists a polynomial-time exact algorithm, we can study large system sizes of up to 10^6 nodes. We measure the capacity and the energy of the resulting optimum matchings. First, we confirm previous analytical results for bipartite regular graphs. Next, we study the finite-size behaviour of the matching capacity and find the same scaling behaviour as before for standard matching, which indicates the universality of the problem. Finally, we investigate for bipartite Erdős–Rényi random graphs the saturability as a function of the average degree, i.e. whether the network allows as many customers as possible to be served, i.e. exploiting the servers in an optimal way. We find phase transitions between unsaturable and saturable phases. These coincide with a strong change of the running time of the exact matching algorithm, as well with the point where a minimum-degree heuristic algorithm starts to fail.Graphical

Envy-free matchings in bipartite graphs and their applications to fair division

A matching in a bipartite graph with parts X and Y is called envy-free, if no unmatched vertex in X is a adjacent to a matched vertex in Y. Every perfect matching is envy-free, but envy-free matchings exist even when perfect matchings do not. We prove that every bipartite graph has a unique partition such that all envy-free matchings are contained in one of the partition sets. Using this structural theorem, we provide a polynomial-time algorithm for finding an envy-free matching of maximum cardinality. For edge-weighted bipartite graphs, we provide a polynomial-time algorithm for finding a maximum-cardinality envy-free matching of minimum total weight. We show how envy-free matchings can be used in various fair division problems with either continuous resources (“cakes”) or discrete ones. In particular, we propose a symmetric algorithm for proportional cake-cutting, an algorithm for 1-out-of-(2n-2) maximin-share allocation of discrete goods, and an algorithm for 1-out-of-⌊2n/3⌋ maximin-share allocation of discrete bads among n agents.

Frequency analysis of load modulation networks for asymmetric Doherty power amplifiers in GaN

AbstractThis paper investigates the frequency response of load modulation networks for asymmetric Doherty power amplifiers (ADPA) with an output back-off power level larger than 6 dB and a power ratio of peak to main amplifier (N − 1) larger than 1. The influence of the main path impedance transformer (IT) on the Doherty impedances at main and peak path as well as on the ADPA's efficiency is analyzed. Scaling of the main IT's characteristic impedance via ξ indicates a maximum broadband matching for an input voltage Vin of ξ · Vin,max. By weighting the frequency- and ξ-dependent efficiency curves using a probability density function (PDF), an optimum is obtained for ξ = 1/N. To verify the theory, three ADPAs with different ξ-scaled ITs are designed, measured, and compared. For the design at 3.6 GHz, a gallium nitride (GaN) transistor is used. By means of the intrinsic node matching technique, matching at the current source plane is obtained. In laboratory measurements, the ADPA with ξ = 1/N achieves a power-added efficiency (PAE) of 63% at 42 dBm output power and a PDF-weighted average PAE of 38.8% within 400 MHz bandwidth for 8 dB peak-to-average power ratio. Comparison with similar state-of-the-art ADPAs in GaN technology shows highest PAE and operation power gain GP for center frequencies larger than 3.0 GHz.

Ancestral Flowering Plant Chromosomes and Gene Orders Based on Generalized Adjacencies and Chromosomal Gene Co-Occurrences.

Recurrent whole genome duplication and the ensuing loss of redundant genes-fractionation-complicate efforts to reconstruct the gene orders and chromosomes of the ancestors associated with the nodes of a phylogeny. Loss of genes disrupts the gene adjacencies key to current techniques. With our RACCROCHE pipeline, instead of starting with the inference of short ancestral segments, we suggest delaying the choice of gene adjacencies while we accumulate many more syntenically validated generalized (gapped) adjacencies. We obtain longer ancestral contigs using maximum weight matching (MWM). Similarly, we do not construct chromosomes by successively piecing together contigs into larger segments, but rather compile counts of pairwise contig co-occurrences on the set of extant genomes and use these to cluster the contigs. Chromosome-level contig assemblies for a monoploid genome emerge naturally at each node of the phylogeny and the contigs then can be ordered along the chromosome. Sampling alternative MWM solutions, visualizing heat maps, and applying gap statistics allow us to estimate the number of chromosomes in the reconstruction. We introduce several measures of quality: length of contigs, continuity of contig structure on successive ancestors, coverage of the extant genome by the reconstruction, and rearrangement relations among the inferred chromosomes. The reconstructed ancestors are visualized by painting the ancestral projections on the descendant genomes. We submit genomes drawn from a broad range of monocot orders to our pipeline, confirming the tetraploidization event "tau" in the stem lineage between the alismatids and the lilioids. We show additional applications to the Solanaceae and to four Brassica genomes, producing evidence about the monoploid ancestor in each case.

Lower Bounds for Maximal Matchings and Maximal Independent Sets

There are distributed graph algorithms for finding maximal matchings and maximal independent sets in O ( Δ + log * n ) communication rounds; here, n is the number of nodes and Δ is the maximum degree. The lower bound by Linial (1987, 1992) shows that the dependency on n is optimal: These problems cannot be solved in o (log * n ) rounds even if Δ = 2. However, the dependency on Δ is a long-standing open question, and there is currently an exponential gap between the upper and lower bounds. We prove that the upper bounds are tight. We show that any algorithm that finds a maximal matching or maximal independent set with probability at least 1-1/ n requires Ω (min { Δ , log log n / log log log n }) rounds in the LOCAL model of distributed computing. As a corollary, it follows that any deterministic algorithm that finds a maximal matching or maximal independent set requires Ω (min { Δ , log n / log log n }) rounds; this is an improvement over prior lower bounds also as a function of n .

Preservation of shared backup path ink‐node content based elastic optical datacenter networks

AbstractEfficient path selection and content availability in the optical datacenter networks are essential for business continuity. To measure quantitatively the connectivity of content and give protection to diverse type of contents, the idea ofk‐node content connectivity is becoming popular. However, the assignment of dedicated spectrum for each end‐to‐end content path consumes too many resources. In order to enhance the resource efficiency, the spectrum can be shared between end‐to‐content paths of various requests. The spectrum sharing minimizes the backup spectrum requirement and has been a topic of research. In this study, an innovative model, namely, end‐to‐end content connectivity based quasi‐bipartite graphs (E‐QBG) for the possible path prediction and maximum matching by Hungarian path prediction (MM‐HPP) are implemented for the spectrum efficiency and the disaster resilient datacenter networks. The objective is to minimize the entire backup spectrum resource and operations path. The quasi‐bipartite graph is used for the end‐to‐end content backup route evaluation including spectrum sharing on various links, while the Hungarian algorithm is utilized for accurate maximum matching prediction between various end‐to‐end route sets. We introduce the concept of maximum dissortativity path based on the weight factor. The proposed E‐QBG and MM‐HPP reduces spectrum consumption which guarantees survivability against multi‐failure and natural disasters. This method leads to an approach for more effective utilization of the resources for end‐to‐end content connected elastic optical datacenter networks as compared with the existing techniques.

A Deamortization Approach for Dynamic Spanner and Dynamic Maximal Matching

Many dynamic graph algorithms have an amortized update time, rather than a stronger worst-case guarantee. But amortized data structures are not suitable for real-time systems, where each individual operation has to be executed quickly. For this reason, there exist many recent randomized results that aim to provide a guarantee stronger than amortized expected. The strongest possible guarantee for a randomized algorithm is that it is always correct (Las Vegas) and has high-probability worst-case update time, which gives a bound on the time for each individual operation that holds with high probability. In this article, we present the first polylogarithmic high-probability worst-case time bounds for the dynamic spanner and the dynamic maximal matching problem. (1) For dynamic spanner, the only known o ( n ) worst-case bounds were O ( n 3/4 ) high-probability worst-case update time for maintaining a 3-spanner and O ( n 5/9 ) for maintaining a 5-spanner. We give a O (1) k log 3 ( n ) high-probability worst-case time bound for maintaining a ( 2k-1 )-spanner, which yields the first worst-case polylog update time for all constant k . (All the results above maintain the optimal tradeoff of stretch 2k-1 and Õ( n 1+1/k ) edges.) (2) For dynamic maximal matching, or dynamic 2-approximate maximum matching, no algorithm with o(n) worst-case time bound was known and we present an algorithm with O (log 5 ( n )) high-probability worst-case time; similar worst-case bounds existed only for maintaining a matching that was (2+ϵ)-approximate, and hence not maximal. Our results are achieved using a new approach for converting amortized guarantees to worst-case ones for randomized data structures by going through a third type of guarantee, which is a middle ground between the two above: An algorithm is said to have worst-case expected update time ɑ if for every update σ, the expected time to process σ is at most ɑ. Although stronger than amortized expected, the worst-case expected guarantee does not resolve the fundamental problem of amortization: A worst-case expected update time of O(1) still allows for the possibility that every 1/ f(n) updates requires ϴ ( f(n) ) time to process, for arbitrarily high f(n) . In this article, we present a black-box reduction that converts any data structure with worst-case expected update time into one with a high-probability worst-case update time: The query time remains the same, while the update time increases by a factor of O (log 2(n) ). Thus, we achieve our results in two steps: (1) First, we show how to convert existing dynamic graph algorithms with amortized expected polylogarithmic running times into algorithms with worst-case expected polylogarithmic running times. (2) Then, we use our black-box reduction to achieve the polylogarithmic high-probability worst-case time bound. All our algorithms are Las-Vegas-type algorithms.