Online Matching Algorithm Research Articles

Matching on the Line Admits no \(o(\sqrt {\log n})\) -Competitive Algorithm

We present a simple proof that no randomized online matching algorithm for the line can be \((\sqrt {\log _2(n+1)}/15)\) -competitive against an oblivious adversary for any n = 2 i - 1 : i ∈ ℕ. This is the first super-constant lower bound for the problem, and disproves as a corollary a recent conjecture on the topology-parametrized competitiveness achievable on generic spaces.

Rawlsian Fairness in Online Bipartite Matching: Two-Sided, Group, and Individual

Online bipartite-matching platforms are ubiquitous and find applications in important areas such as crowdsourcing and ridesharing. In the most general form, the platform consists of three entities: two sides to be matched and a platform operator that decides the matching. The design of algorithms for such platforms has traditionally focused on the operator’s (expected) profit. Since fairness has become an important consideration that was ignored in the existing algorithms a collection of online matching algorithms have been developed that give a fair treatment guarantee for one side of the market at the expense of a drop in the operator’s profit. In this paper, we generalize the existing work to offer fair treatment guarantees to both sides of the market simultaneously, at a calculated worst case drop to operator profit. We consider group and individual Rawlsian fairness criteria. Moreover, our algorithms have theoretical guarantees and have adjustable parameters that can be tuned as desired to balance the trade-off between the utilities of the three sides. We also derive hardness results that give clear upper bounds over the performance of any algorithm.

Fairness Maximization among Offline Agents in Online-Matching Markets

Online matching markets (OMMs) are commonly used in today’s world to pair agents from two parties (whom we will call offline and online agents) for mutual benefit. However, studies have shown that the algorithms making decisions in these OMMs often leave disparities in matching rates, especially for offline agents. In this article, we propose online matching algorithms that optimize for either individual or group-level fairness among offline agents in OMMs. We present two linear-programming (LP) based sampling algorithms, which achieve competitive ratios at least 0.725 for individual fairness maximization and 0.719 for group fairness maximization. We derive further bounds based on fairness parameters, demonstrating conditions under which the competitive ratio can increase to 100%. There are two key ideas helping us break the barrier of 1-1/𝖾~ 63.2% for competitive ratio in online matching. One is boosting , which is to adaptively re-distribute all sampling probabilities among only the available neighbors for every arriving online agent. The other is attenuation , which aims to balance the matching probabilities among offline agents with different mass allocated by the benchmark LP. We conduct extensive numerical experiments and results show that our boosted version of sampling algorithms are not only conceptually easy to implement but also highly effective in practical instances of OMMs where fairness is a concern.

Correction to: Markovian Online Matching Algorithms on Large Bipartite Random Graphs

Correction to: Markovian Online Matching Algorithms on Large Bipartite Random Graphs

Edge-Weighted Online Bipartite Matching

Online bipartite matching is one of the most fundamental problems in the online algorithms literature. Karp, Vazirani, and Vazirani (STOC 1990) gave an elegant algorithm for unweighted bipartite matching that achieves an optimal competitive ratio of 1-1/e . Aggarwal et al. (SODA 2011) later generalized their algorithm and analysis to the vertex-weighted case. Little is known, however, about the most general edge-weighted problem aside from the trivial 1/2-competitive greedy algorithm. In this article, we present the first online algorithm that breaks the long-standing 1/2 barrier and achieves a competitive ratio of at least 0.5086. In light of the hardness result of Kapralov, Post, and Vondrák (SODA 2013), which restricts beating a 1/2 competitive ratio for the more general monotone submodular welfare maximization problem, our result can be seen as strong evidence that edge-weighted bipartite matching is strictly easier than submodular welfare maximization in an online setting. The main ingredient in our online matching algorithm is a novel subroutine called online correlated selection (OCS), which takes a sequence of pairs of vertices as input and selects one vertex from each pair. Instead of using a fresh random bit to choose a vertex from each pair, the OCS negatively correlates decisions across different pairs and provides a quantitative measure on the level of correlation. We believe our OCS technique is of independent interest and will find further applications in other online optimization problems.

Markovian Online Matching Algorithms on Large Bipartite Random Graphs

In this paper, we present an approximation of the matching coverage on large bipartite graphs, for local online matching algorithms based on the sole knowledge of the remaining degree of the nodes of the graph at hand. This approximation is obtained by applying the Differential Equation Method to a measure-valued process representing an alternative construction, in which the matching and the graph are constructed simultaneously, by a uniform pairing leading to a realization of the bipartite Configuration Model. The latter auxiliary construction is shown to be equivalent in distribution to the original one. It allows to drastically reduce the complexity of the problem, in that the resulting matching coverage can be written as a simple function of the final value of the process, and in turn, approximated by a simple function of the solution of a system of ODE’s. By way of simulations, we illustrate the accuracy of our estimate, and then compare the performance of an algorithm based on the minimal residual degree of the nodes, to the classical greedy matching.

Online stochastic weighted matching algorithm for real‐time shared parking

AbstractParking management plays an important role in the efficiency of transportation systems. We study the problem of matching shared parking slots with demanders online on a parking platform with the aim of managing parking spaces intelligently and efficiently. In our setting, the demanders submitting parking requests sequentially are assumed to be drawn from a distribution over demander types. No further assumptions about the demander arrival stream are needed. Matching decisions are triggered by arrival events instead of time points. This benefits the demanders by immediate responses to parking requests. An online matching algorithm is designed to make real‐time decisions and maximize social welfare. We demonstrated that the algorithm has a large competitive ratio, which implies a good performance of the algorithm. Numerical experiments are conducted to further examine the performance of the algorithm. The experimental results show that our proposed algorithm can achieve such a large competitive ratio in a real‐time matching way as the batch matching algorithm does in a serious delay matching way.

Applications of Nondominated Sorting Genetic Algorithm II Combined with WKNN Online Matching Algorithm in Building Indoor Optimization Design.

The present work aims to improve the comfort of architectural interior design and reduce indoor energy consumption. The Weight K-Nearest Neighborhood (WKNN) algorithm and Nondominated Sorting Genetic algorithm are proposed to locate and analyze the spatial location of indoor personnel and optimize the indoor energy consumption in combination with residential behavior. Firstly, the indoor human behavior data and energy-saving problems are analyzed based on residential behavior theory and architectural physics. The indoor positioning algorithm is proposed to identify the personnel activities to realize the optimization of indoor energy distribution. Secondly, mean filtering and cluster analysis are adopted to optimize sampling points' data and fingerprint database to eliminate data noise. Besides, the WKNN algorithm is used for Wireless Fidelity (Wi-Fi) indoor location fingerprint location. Then, aiming at the multiobjective optimization problem of building indoor energy consumption, the Nondominated Sorting Genetic algorithm obtains the optimal solution of the model. Combined with the indoor location information of personnel, the indoor heating and cooling system is monitored and distributed to reduce the energy consumption in the building while ensuring the living comfort of personnel. The test and simulation results demonstrate that the mean filtering algorithm can solve the room's fluctuation problem of Wi-Fi signals. The cluster analysis algorithm can eliminate the data noise of the fingerprint database and improve the positioning accuracy of the positioning algorithm. Moreover, the location result is independent of the number of nodes; the number of sampling points does not affect the location result. The positioning accuracy of the WKNN algorithm is 2 m, and the positioning error rate within 2 m is about 60%. Compared with other algorithms, the WKNN algorithm has better positioning accuracy and positioning stability. Therefore, the location algorithm designed here can be applied to indoor location optimization. This study provides a reference for optimizing buildings' indoor positioning and energy consumption.

Online Multiple Athlete Tracking with Pose-Based Long-Term Temporal Dependencies.

This paper addresses the Multi-Athlete Tracking (MAT) problem, which plays a crucial role in sports video analysis. There exist specific challenges in MAT, e.g., athletes share a high similarity in appearance and frequently occlude with each other, making existing approaches not applicable for this task. To address this problem, we propose a novel online multiple athlete tracking approach which make use of long-term temporal pose dynamics for better distinguishing different athletes. Firstly, we design a Pose-based Triple Stream Network (PTSN) based on Long Short-Term Memory (LSTM) networks, capable of modeling long-term temporal pose dynamics of athletes, including pose-based appearance, motion and athletes’ interaction clues. Secondly, we propose a multi-state online matching algorithm based on bipartite graph matching and similarity scores produced by PTSN. It is robust to noisy detections and occlusions due to the reliable transitions of multiple detection states. We evaluate our method on the APIDIS, NCAA Basketball and VolleyTrack databases, and the experiment results demonstrate its effectiveness.

Online Algorithms for Dynamic Matching Markets in Power Distribution Systems

This letter proposes online algorithms for dynamic matching markets in power distribution systems. These algorithms address the problem of matching flexible loads with renewable generation, with the objective of maximizing social welfare of the exchange in the system. More specifically, two online matching algorithms are proposed for two generation-load scenarios: (i) when the mean of renewable generation is greater than the mean of the flexible load, and (ii) when the condition (i) is reversed. With the intuition that the performance of such algorithms degrades with increasing randomness of the supply and demand, two properties are proposed for assessing the performance of the algorithms. First property is convergence to optimality (CO) as the underlying randomness of renewable generation and customer loads goes to zero. The second property is deviation from optimality, which is measured as a function of the standard deviation of the underlying randomness of renewable generation and customer loads. The algorithm proposed for the first scenario is shown to satisfy CO and a deviation from optimality that varies linearly with the variation in the standard deviation. We then show that the algorithm proposed for the second scenario satisfies CO and a deviation from optimality that varies linearly with the variation in standard deviation plus an offset under certain condition.

Privacy preserving online matching on ridesharing platforms

Ridesharing platforms, as typical applications of spatial crowdsourcing, are becoming more and more popular in the era of mobile internet and sharing economy. One of the most fundamental issues on ridesharing platforms is to assign orders to drivers, which can be naturally modeled as online bipartite matching problem. However, conventional online matching algorithms usually lack data privacy protection mechanisms. This has become a serious issue since the spatiotemporal data of passengers is often sensitive. New policies such as EU’s General Data Protection Regulation (GDPR) also enforce protection of sensitive data, which further exacerbate the privacy issues. To deal with the problems, in this paper we propose a framework based on differential privacy (DP) techniques to preserve the privacy of individuals on ridesharing platforms. Specifically, we devise a novel approach to perturb locations in online minimum bipartite matching problem and theoretically show that the performance of the perturbed matching algorithm has the same magnitude with the unperturbed one. Experiments conducted on real datasets have also shown the effectiveness of proposed framework.

Mobile robot motion control and autonomous navigation in GPS-denied outdoor environments using 3D laser scanning

Purpose This paper aims to propose a series of approaches to solve the problem of the mobile robot motion control and autonomous navigation in large-scale outdoor GPS-denied environments. Design/methodology/approach Based on the model of mobile robot with two driving wheels, a controller is designed and tested in obstacle-cluttered scenes in this paper. By using the priori “topology-geometry” map constructed based on the odometer data and the online matching algorithm of 3D-laser scanning points, a novel approach of outdoor localization with 3D-laser scanner is proposed to solve the problem of poor localization accuracy in GPS-denied environments. A path planning strategy based on geometric feature analysis and priority evaluation algorithm is also adopted to ensure the safety and reliability of mobile robot’s autonomous navigation and control. Findings A series of experiments are conducted with a self-designed mobile robot platform in large-scale outdoor environments, and the experimental results show the validity and effectiveness of the proposed approach. Originality/value The problem of motion control for a differential drive mobile robot is investigated in this paper first. At the same time, a novel approach of outdoor localization with 3D-laser scanner is proposed to solve the problem of poor localization accuracy in GPS-denied environments. A path planning strategy based on geometric feature analysis and priority evaluation algorithm is also adopted to ensure the safety and reliability of mobile robot’s autonomous navigation and control.

A $${o}\mathopen {}\left( n\right) \mathclose {}$$-Competitive Deterministic Algorithm for Online Matching on a Line

Online matching on a line involves matching an online stream of requests to a given set of servers, all in the real line, with the objective of minimizing the sum of the distances between matched server-request pairs. The best previously known upper and lower bounds on the optimal deterministic competitive ratio are linear in the number of requests, and constant, respectively. We show that online matching on a line is essentially equivalent to a particular search problem, which we call k-lost-cows. We then obtain the first deterministic sub-linearly competitive algorithm for online matching on a line by giving such an algorithm for the k-lost-cows problem.

Decentralized Coded Caching Without File Splitting

Coded caching is an effective technique to reduce the redundant traffic in wireless networks. The existing coded caching schemes require the splitting of files into a possibly large number of subfiles, i.e., they perform coded subfile caching. Keeping the files intact during the caching process would actually be appealing, broadly speaking because of its simpler implementation. However, little is known about the effectiveness of this coded file caching in reducing the data delivery rate. In this paper, we propose such a file caching scheme which uses a decentralized algorithm for content placement and either an online clique cover or matching algorithm for the delivery of missing data. We derive approximations for the expected delivery rate of both schemes using the differential equations method, and show them to be tight through concentration analysis and computer simulations. Our numerical results demonstrate that the proposed coded file caching is significantly more effective than uncoded caching in reducing the delivery rate. We furthermore show the additional improvement in the performance of the proposed scheme when its application is extended to subfile caching with a small number of subfiles.

Relax online resource allocation algorithms for D2D communication

SummaryMaximizing the system sumrate by sharing the resource blocks among the cellular user equipments and the D2D (device to device) pairs while maintaining the quality of service is an important research question in a D2D communication underlaying cellular networks. The problem can be optimally solved in offline by using the weighted bipartite matching algorithm. However, in long‐term evolution and beyond (4G and 5G) systems, scheduling algorithms should be very efficient where the optimal algorithm is quite complex to implement. Hence, a low complexity algorithm that returns almost the optimal solution can be an alternative to this research problem. In this paper, we propose 2 less complex stable matching–based relax online algorithms those exhibit very close to the optimal solution. Our proposed algorithms deal with fixed number of cellular user equipments and a variable number of D2D pairs those arrive in the system online. Unlike online matching algorithms, we consider that an assignment can be revoked if it improves the objective function (total system sumrate). However, we want to minimize the number of revocation (ie, the number of changes in the assignments) as a large number of changes can be expensive for the networks too. We consider various offline algorithms proposed for the same research problem as relaxed online algorithms. Through extensive simulations, we find that our proposed algorithms outperform all of the algorithms in terms of the number of changes in assignment between 2 successive allocations while maintaining the total system sumrate very close to the optimal algorithm.

Parallel algorithms for flexible pattern matching on big graphs

Strong simulation is a state-of-the-art approximate scheme in graph pattern matching. This scheme always finds high-quality results compared to other schemes. However, as the Web and social networks are increasingly used in human lives, the scale of the data grows extremely large. As a result, such big graphs are often stored in the distributed environment, in order to be managed efficiently. Unfortunately, current distributed algorithm for strong simulation is not efficient and cannot be applied to real applications. In this paper, we propose efficient parallel algorithms for strong simulation in the distributed setting. The contribution includes (1) We convert the calculation of strong simulation to calculating a relative small set of partial results for each partition of pattern suitable for distributed system. (2) We develop a method to reduce data shipment and time complexity of local computation in the distributed setting. (3) We split the distributed calculation of strong simulation into an offline redistribution algorithm and an online matching algorithm. The major data shipment is involved in the offline algorithm, while the online algorithm is highly parallel and much more efficient than current algorithms. (4) By experiments on both real and synthetic data, we verify the efficiency of our distributed algorithms and the effectiveness of our scheme without large intermediate results.

The Value-of-Information in Matching With Queues

We consider the problem of optimal matching with queues in dynamic systems and investigate the value-of-information. In such systems, operators match tasks and resources stored in queues, with the objective of maximizing the system utility of the matching reward profile, minus the average matching cost. This problem appears in many practical systems and the main challenges are the no-underflow constraints, and the lack of matching-reward information and system dynamics statistics. We develop two online matching algorithms: Learning-aided Reward optimAl Matching ( $\mathtt {LRAM}$ ) and Dual- $\mathtt {LRAM}$ ( $\mathtt {DRAM}$ ) to effectively resolve both challenges. Both algorithms are equipped with a learning module for estimating the matching-reward information, while $\mathtt {DRAM}$ incorporates an additional module for learning the system dynamics. We show that both algorithms achieve an $O(\epsilon +\delta _{r})$ close-to-optimal utility performance for any $\epsilon >0$ , while $\mathtt {DRAM}$ achieves a faster convergence speed and a better delay compared with $\mathtt {LRAM}$ , i.e., $O(\delta _{\pi }/\epsilon + \log (1/\epsilon )^{2})$ delay and $O(\delta _{\pi }/\epsilon )$ convergence under $\mathtt {DRAM}$ compared with $O(1/\epsilon )$ delay and convergence under $\mathtt {LRAM}$ ( $\delta _{r}$ and $\delta _{\pi }$ are maximum estimation errors for reward and system dynamics). Our results show that the information of different system components can play very different roles in algorithm performance and provide a novel way for designing the joint learning-control algorithms.

On optimization of expertise matching with various constraints

This paper studies the problem of expertise matching with various constraints. Expertise matching, which aims to find the alignment between experts and queries, is a common problem in many applications such as conference paper–reviewer assignment, product–reviewer alignment, and product-endorser matching. Most existing methods formalize this problem as an information-retrieval problem and focus on finding a set of experts for each query independently. However, in real-world systems, various constraints are often needed to be considered. For example, in order to review a paper, it is desirable that there is at least one senior reviewer to guide the reviewing process. An important question is: “Can we design a framework to efficiently find the optimal solution for expertise matching under various constraints?” This paper explores such an approach by formulating the expertise matching problem in a constraint-based optimization framework. In the proposed framework, the problem of expertise matching is linked to a convex cost flow problem, which guarantees an optimal solution under various constraints. We also present an online matching algorithm to support incorporating user feedbacks in real time. The proposed approach has been evaluated on two different genres of expertise matching problems, namely conference paper–reviewer assignment and teacher–course assignment. Experimental results validate the effectiveness of the proposed approach. Based on the proposed method, we have also developed an online system for paper–reviewer suggestions, which has been used for paper–reviewer assignment in a top conference and feedbacks from the conference organizers are very positive.

Variations on Muchnik’s Conditional Complexity Theorem

Muchnik’s theorem about simple conditional descriptions states that for all strings a and b there exists a program p transforming a to b that has the least possible length and is simple conditional on b. In this paper we present two new proofs of this theorem. The first one is based on the on-line matching algorithm for bipartite graphs. The second one, based on extractors, can be generalized to prove a version of Muchnik’s theorem for space-bounded Kolmogorov complexity. Another version of Muchnik’s theorem is proven for a resource-bounded variant of Kolmogorov complexity based on Arthur–Merlin protocols.

MOODS: fast search for position weight matrix matches in DNA sequences

Summary: MOODS (MOtif Occurrence Detection Suite) is a software package for matching position weight matrices against DNA sequences. MOODS implements state-of-the-art online matching algorithms, achieving considerably faster scanning speed than with a simple brute-force search. MOODS is written in C++, with bindings for the popular BioPerl and Biopython toolkits. It can easily be adapted for different purposes and integrated into existing workflows. It can also be used as a C++ library.Availability: The package with documentation and examples of usage is available at http://www.cs.helsinki.fi/group/pssmfind. The source code is also available under the terms of a GNU General Public License (GPL).Contact: janne.h.korhonen@helsinki.fi