Weight Bipartite Matching Research Articles

A Dual-Archive Memetic Algorithm for Unrelated Parallel-Machine Scheduling to Minimize Total Weighted Flow Time and Weighted Tardiness

This paper presents an effective approach to solving unrelated parallel-machine scheduling problems that minimizes two aggregation objectives: total weighted flow time and total weighted tardiness. At each iteration step, the approach partitions the objective space using different weights on each objective, and applies weighted bipartite matching (WBM) to find the best neighborhood solution in each objective subspace. Three algorithms are used to assess this approach: NSGAII, SPEA2, and DAMA (dual-archive memetic algorithm). When using WBM, weighted apparent tardiness cost with setups (W-ATCS) is employed to solve single machine scheduling problems. For DAMA, two dissimilar archives are maintained at each generation: one archive preserves efficient solutions, the other preserves inefficient solutions, and the two archives compete to produce next generation offspring. An experiment was conducted to evaluate the proposed approach based on several performance metrics. The results indicate that decoding scheme using WBM will produce significantly better solutions, regardless of which algorithm is employed. The results also show that using random weights (RW) on objectives for evolution excels using fixed weights (FW). Finally, DAMA_RW outperforms all other algorithms based on the same number of calculated solutions.

Mining User Movement Behavior Patterns in a Mobile Service Environment

Mobile service systems offer users useful information ubiquitously via mobile devices. Based on changeable user movement behavior patterns (UMBPs), mobile service systems have the capability of effectively mining a special request from abundant data. In this paper, UMBPs are studied in terms of the problem of mining matching mobile access patterns based on joining the following four kinds of characteristics, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> , and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> , where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U</i> is the mobile user, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> is the movement location, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> is the dwell time in the timestamp, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> is the service request. By introducing standard graph-matching algorithms along with the primitives of a database management system, which comprises grouping, sorting, and joining, these joint operations are defined. Moreover, by mining the associated structure via maximum weight bipartite graph matching, a prediction mechanism, based on the model of UMBPs, is utilized to find strong relationships among <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> , and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> . In addition, a PC-based experimental evaluation under various simulation conditions, using synthetically generated data, is introduced. Finally, performance studies are conducted to show that, in terms of execution efficiency and scalability, the proposed procedures produced excellent performance results.

Streaming Graph Computations with a Helpful Advisor

Motivated by the trend to outsource work to commercial cloud computing services, we consider a variation of the streaming paradigm where a streaming algorithm can be assisted by a powerful helper that can provide annotations to the data stream. We extend previous work on such annotation models by considering a number of graph streaming problems. Without annotations, streaming algorithms for graph problems generally require significant memory; we show that for many standard problems, including all graph problems that can be expressed with totally unimodular integer programming formulations, only constant space (measured in words) is needed for single-pass algorithms given linear-sized annotations. We also obtain protocols achieving essentially optimal tradeoffs between annotation length and memory usage for several important problems, including integer matrix-vector multiplication, as well as shortest s-t path in small-diameter graphs. We also obtain non-trivial tradeoffs for minimum weight bipartite perfect matching and shortest s-t path in general graphs.

Virtual multi-fracture craniofacial reconstruction using computer vision and graph matching

The problem of computer vision-guided reconstruction of a fractured human mandible from a computed tomography (CT) image sequence exhibiting multiple broken fragments is addressed. The problem resembles 3D jigsaw puzzle assembly and hence is of general interest for a variety of applications dealing with automated reconstruction or assembly. The specific problem of automated multi-fracture craniofacial reconstruction is particularly challenging since the identification of opposable fracture surfaces followed by their pairwise registration needs to be performed expeditiously in order to minimize the operative trauma to the patient and also limit the operating costs. A polynomial time solution using graph matching is proposed. In the first phase of the proposed solution, the opposable fracture surfaces are identified using the Maximum Weight Graph Matching algorithm. The pairs of opposable fracture surfaces, identified in the first stage, are registered in the second phase using the Iterative Closest Point (ICP) algorithm. Correspondence for a given pair of fracture surfaces, needed for the Closest Set computation in the ICP algorithm, is established using the Maximum Cardinality Minimum Weight bipartite graph matching algorithm. The correctness of the reconstruction is constantly monitored by using constraints derived from a volumetric matching procedure guided by the computation of the Tanimoto Coefficient.

Virtual craniofacial reconstruction using computer vision, graph theory and geometric constraints

A novel solution to the problem of virtual craniofacial reconstruction using computer vision, graph theory and geometric constraints is proposed. Virtual craniofacial reconstruction is modeled along the lines of the well-known problem of rigid surface registration. The Iterative Closest Point (ICP) algorithm is first employed with the closest set computation performed using the Maximum Cardinality Minimum Weight (MCMW) bipartite graph matching algorithm. Next, the bounding boxes of the fracture surfaces, treated as cycle graphs, are employed to generate multiple candidate solutions based on the concept of graph automorphism. The best candidate solution is selected by exploiting local and global geometric constraints. Finally, the initialization of the ICP algorithm with the best candidate solution is shown to improve surface reconstruction accuracy and speed of convergence. Experimental results on Computed Tomography (CT) scans of real patients are presented.

Modified bipartite matching for multiobjective optimization: Application to antenna assignments in MIMO systems

Based on the Hungarian algorithm, the Kuhn-Munkres algorithm can provide the maximum weight bipartite matching for assignment problems. However, it can only solve the single objective optimization problem. In this paper, we formulate the multi-objective optimization (MO) problem for bipartite matching, and propose a modified bipartite matching (MBM) algorithm to approach the Pareto set with a low computational complexity and to dynamically select proper solutions with given constraints among the reduced matching set. In addition, our MBM algorithm is extended to the case of asymmetric bipartite graphs. Finally, we illustrate the application of MBM to antenna assignments in wireless multiple-input multiple-output (MIMO) systems for both symmetric and asymmetric scenarios, where we consider the multi-objective optimization problem with the maximization of the system capacity, total traffic priority, and long-term fairness among all mobile users. The simulation results show that MBM can effectively reduce the matching set and dynamically provide the optimized performance with different quality of service (QoS) requirements.

Tracking in a spaghetti bowl

The problem of tracking end-to-end service-level transactions in the absence of instrumentation support is considered. The transaction instances progress through a state-transition model and generate time-stamped footprints on entering each state in the model. The goal is to track individual transactions using these footprints even when the footprints may not contain any tokens uniquely identifying the transaction instances that generated them. Assuming a semi-Markov process model for state transitions, the transaction instances are tracked probabilistically by matching them to the available footprints according to the maximum likelihood (ML) criterion. Under the ML-rule, for a two-state system, it is shown that the probability that all the instances are matched correctly is minimized when the transition times are i.i.d. exponentially distributed. When the transition times are i.i.d. distributed, the ML-rule reduces to a minimum weight bipartite matching and reduces further to a first-in first-out match for a special class of distributions. For a multi-state model with an acyclic state transition digraph, a constructive proof shows that the ML-rule reduces to splicing the results of independent matching of many bipartite systems.

An Optimal Graph Theoretic Approach to Data Association in SLAM

In this paper, we study the problem of data association in simultaneous localization and mapping (SLAM). Since almost all existing methods for solving the problem are only able to provide suboptimal solutions, we revisit this problem and propose an optimal graph approach to resolve it. We first formulate the problem as integer programming (IP) problem, and then algorithmically prove that the IP is equivalent to a minimum weight bipartite perfect matching problem. Thus, optimally solving the bipartite matching problem is equivalent to optimally resolve the IP problem (i.e., the data association problem). Simulations validate the effectiveness and accuracy of the proposed approach.

Distributed‐ and shared‐memory parallelizationsof assignment‐based data association formultitarget tracking

To date, there has been a lack of efficient and practical distributed‐ and shared‐memoryparallelizations of the data association problem for multitarget tracking. Filling this gap is oneof the primary focuses of the present work. We begin by describing our data association algorithmin terms of an Interacting Multiple Model (IMM) state estimator embedded into anoptimization framework, namely, a two‐dimensional (2D) assignment problem (i.e., weightedbipartite matching). Contrary to conventional wisdom, we show that the data association (oroptimization) problem is not the major computational bottleneck; instead, the interface to theoptimization problem, namely, computing the rather numerous gating tests and IMM stateestimates, covariance calculations, and likelihood function evaluations (used as cost coefficientsin the 2D assignment problem), is the primary source of the workload. Hence, for both ageneral-purpose shared‐memory MIMD (Multiple Instruction Multiple Data) multiprocessorsystem and a distributed‐memory Intel Paragon high‐performance computer, we developedparallelizations of the data association problem that focus on the interface problem. For theformer, a coarse‐grained dynamic parallelization was developed that realizes excellent performance(i.e., superlinear speedups) independent of numerous factors influencing problemsize (e.g., many models in the IMM, denseycluttered environments, contentious target‐measurementdata, etc.). For the latter, an SPMD (Single Program Multiple Data) parallelization wasdeveloped that realizes near‐linear speedups using relatively simple dynamic task allocationalgorithms. Using a real measurement database based on two FAA air traffic control radars, weshow that the parallelizations developed in this work offer great promise in practice.

Achieving 100% throughput in an input-queued switch

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

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

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