Bipartite Matching Algorithm Research Articles

Heuristic initialization for bipartite matching problems

It is a well-established result that improved pivoting in linear solvers can be achieved by computing a bipartite matching between matrix entries and positions on the main diagonal. With the availability of increasingly faster linear solvers, the speed of bipartite matching computations must keep up to avoid slowing down the main computation. Fast algorithms for bipartite matching, which are usually initialized with simple heuristics, have been known for a long time. However, the performance of these algorithms is largely dependent on the quality of the heuristic. We compare combinations of several known heuristics and exact algorithms to find fast combined methods, using real-world matrices as well as randomly generated instances. In addition, we present a new heuristic aimed at obtaining high-quality matchings and compare its impact on bipartite matching algorithms with that of other heuristics. The experiments suggest that its performance compares favorably to the best-known heuristics, and that it is especially suited for application in linear solvers.

An Optimal Resource Binding Algorithm with Inter-Transition Switching Activities for Low Power

Resource binding, a key step encountered in behavioral synthesis, has been studied intensively in the past. Among the published results, resource binding to reduce switching activity (SA) of the design for minimizing dynamic power has been one of the actively-pursued topics. Two types of SAs can be minimized: the intra-transition SA (occurring during the propagation of a single input vector) and the inter-transition SA (occurring between different input vectors). Previous work either ignored the inter-transition SA or provided heuristic to deal with it. When the inter-transition SA was considered, it was not clear previously whether the problem could still be solved optimally. In this paper, for the first time, we demonstrate that resource binding considering inter-transition SAs can be solved in polynomial time for designs that can be represented by data-flow graphs (DFG). This is realized by transforming the problem into finding the shortest path problem in a k-dimensional graph. We also propose an efficient heuristic that uses a network-flow algorithm followed by a legalization step using a bipartite matching algorithm. Experimental results show that a considerable amount of SA reduction can be obtained compared to the previous state-of-the-art results.

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.

Object handoff between uncalibrated views without planar ground assumption

We present a new method of object handoff between two overlapping views in a visual surveillance system. This method requires neither camera calibration nor planar ground assumption. Our approach is composed of two phases: training a handoff table and running object handoff online. In the first phase, a handoff table which contains point correspondences between two views, is constructed from a pair of image sequences. The point correspondences are obtained by computing the conditional probability that for a point pair, given a point belonging to the foreground region at a time instant, the other also belongs to the foreground region at the same time. In the second phase, the actual object handoff is performed with the help of the table, where an optimal bipartite matching algorithm is applied to resolve matching ambiguity. The experimental results for an outdoor scene and synthetic data are shown.

Analysis of Randomized Scheduling Algorithm for a Practical Bufferless Optical Network

We evaluate a plausible bufferless star-based packet-switched optical network. A randomized scheduling algorithm is used to resolve contention, alleviating the need for a centralized controller to coordinate the edge nodes. A bipartite graph matching algorithm is proposed to be used at the core node to minimize the packet drop rate. We examine the performance of the system via simulation, to establish the potential of this architecture for practical packet-switched optical networks.

Combinatorial Analysis of Singular Matrix Pencils

This paper investigates the Kronecker canonical form of matrix pencils under the genericity assumption that the set of nonzero entries is algebraically independent. We provide a combinatorial characterization of the sums of the row/column indices supported by efficient bipartite matching algorithms. We also give a simple alternative proof for a theorem of Poljak on the generic ranks of matrix powers.

Protein−Ligand NOE Matching: A High-Throughput Method for Binding Pose Evaluation That Does Not Require Protein NMR Resonance Assignments

Given the three-dimensional (3D) structure of a protein, the binding pose of a ligand can be determined using distance restraints derived from assigned intra-ligand and protein-ligand nuclear Overhauser effects (NOEs). A primary limitation of this approach is the need for resonance assignments of the ligand-bound protein. We have developed an approach that utilizes data from 3D 13C-edited, 13C/15N-filtered HSQC-NOESY spectra for evaluating ligand binding poses without requiring protein NMR resonance assignments. Only the 1H NMR assignments of the bound ligand are essential. Trial ligand binding poses are generated by any suitable method (e.g., computational docking). For each trial binding pose, the 3D 13C-edited, 13C/15N-filtered HSQC-NOESY spectrum is predicted, and the predicted and observed patterns of protein-ligand NOEs are matched and scored using a fast, deterministic bipartite graph matching algorithm. The best scoring (lowest "cost") poses are identified. Our method can incorporate any explicit restraints or protein assignment data that are available, and many extensions of the basic procedure are feasible. Only a single sample is required, and the method can be applied to both slowly and rapidly exchanging ligands. The method was applied to three test cases: one complex involving muscle fatty acid-binding protein (mFABP) and two complexes involving the leukocyte function-associated antigen 1 (LFA-1) I-domain. Without using experimental protein NMR assignments, the method identified the known binding poses with good accuracy. The addition of experimental protein NMR assignments improves the results. Our "NOE matching" approach is expected to be widely applicable; i.e., it does not appear to depend on a fortuitous distribution of binding pocket residues.

Clip-based similarity measure for query-dependent clip retrieval and video summarization

This paper proposes a new approach and algorithm for the similarity measure of video clips. The similarity is mainly based on two bipartite graph matching algorithms: maximum matching (MM) and optimal matching (OM). MM is able to rapidly filter irrelevant video clips, while OM is capable of ranking the similarity of clips according to visual and granularity factors. We apply the similarity measure for two tasks: retrieval and summarization. In video retrieval, a hierarchical retrieval framework is constructed based on MM and OM. The validity of the framework is theoretically proved and empirically verified on a video database of 21 h. A query-dependent clip segmentation algorithm is also proposed to automatically locate the potential boundaries of clips in videos. In video summarization, a graph-based clustering algorithm, incorporated with the proposed similarity measure, is adopted to detect the highlighted events reported by different newscasts.

Practical Fast Clock-Schedule Design Algorithms

In this paper, a practical clock-scheduling engine is introduced. The minimum feasible clock-period is obtained by using a modified Bellman-Ford shortest path algorithm. Then an optimum cost clock-schedule is obtained by using a bipartite matching algorithm. It also provides useful information to circuit synthesis tools. The experiment to a circuit with about 10000 registers and 100000 signal paths shows that a result is obtained within a few minutes. The computation time is almost linear to the circuit size in practice.

Revealing divergent evolution, identifying circular permutations and detecting active-sites by protein structure comparison

BackgroundProtein structure comparison is one of the most important problems in computational biology and plays a key role in protein structure prediction, fold family classification, motif finding, phylogenetic tree reconstruction and protein docking.ResultsWe propose a novel method to compare the protein structures in an accurate and efficient manner. Such a method can be used to not only reveal divergent evolution, but also identify circular permutations and further detect active-sites. Specifically, we define the structure alignment as a multi-objective optimization problem, i.e., maximizing the number of aligned atoms and minimizing their root mean square distance. By controlling a single distance-related parameter, theoretically we can obtain a variety of optimal alignments corresponding to different optimal matching patterns, i.e., from a large matching portion to a small matching portion. The number of variables in our algorithm increases with the number of atoms of protein pairs in almost a linear manner. In addition to solid theoretical background, numerical experiments demonstrated significant improvement of our approach over the existing methods in terms of quality and efficiency. In particular, we show that divergent evolution, circular permutations and active-sites (or structural motifs) can be identified by our method. The software SAMO is available upon request from the authors, or from and .ConclusionA novel formulation is proposed to accurately align protein structures in the framework of multi-objective optimization, based on a sequence order-independent strategy. A fast and accurate algorithm based on the bipartite matching algorithm is developed by exploiting the special features. Convergence of computation is shown in experiments and is also theoretically proven.

Sweep synchronization as a global propagation mechanism

This paper presents a new generic filtering algorithm which simultaneously considers n conjunctions of constraints as well as those constraints mentioning some variables Y k of the pairs X , Y k ( 1 ⩽ k ⩽ n ) occurring in these conjunctions. The main benefit of this new technique comes from the fact that, for adjusting the bounds of a variable X according to n conjunctions, we do not perform n sweeps in an independent way but rather synchronize them. We then specialize this technique to the non-overlapping rectangles constraint where we consider the case where several rectangles of height one have the same X coordinate for their origin as well as the same length. For this specific constraint we come up with an incremental bipartite matching algorithm which is triggered while we sweep over the time axis. We illustrate the usefulness of this new pruning method on a timetabling problem, where each task cannot be interrupted and requires the simultaneous availability of n distinct persons. In addition each person has his own periods of unavailability and can only perform one task at a time.

Compressible area fill synthesis

Control of variability and performance in the back end of the VLSI manufacturing line has become extremely difficult with the introduction of new materials such as copper and low-k dielectrics. To improve manufacturability, and in particular to enable more uniform chemical-mechanical planarization (CMP), it is necessary to insert area fill features into low-density layout regions. Because area fill feature sizes are very small compared to the large empty layout areas that need to be filled, the filling process can increase the size of the resulting layout data file by an order of magnitude or more. To reduce file transfer times, and to accommodate future maskless lithography regimes, data compression becomes a significant requirement for fill synthesis. In this paper, we make the following contributions. First, we define two complementary strategies for fill data volume reduction corresponding to two different points in the design-to-manufacturing flow: compressible filling and post-fill compression . Second, we compare compressible filling methods in the fixed-dissection regime when two different sets of compression operators are used: the traditional GDSII array reference (AREF) construct, and the new Open Artwork System Interchange Standard (OASIS) repetitions. We apply greedy techniques to find practical compressible filling solutions and compare them with optimal integer linear programming solutions. Third, for the post-fill data compression problem, we propose two greedy heuristics, an exhaustive search-based method, and a smart spatial regularity search technique. We utilize an optimal bipartite matching algorithm to apply OASIS repetition operators to irregular fill patterns. Our experimental results indicate that both fill data compression methodologies can achieve significant data compression ratios, and that they outperform industry tools such as Calibre V8.8 from Mentor Graphics. Our experiments also highlight the advantages of the new OASIS compression operators over the GDSII AREF construct.

Exact and approximate graph matching using random walks

In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection.

Efficient Algorithms for the Inverse Spanning-Tree Problem

The inverse spanning-tree problem is to modify edge weights in a graph so that a given tree T is a minimum spanning tree. The objective is to minimize the cost of the deviation. The cost of deviation is typically a convex function. We propose algorithms here that are faster than all known algorithms for the problem. Our algorithm's run time for any convex inverse spanning-tree problem is O(nm log2 n) for a graph on n nodes and m edges plus the time required to find the minima of the n convex deviation functions. This not only improves on the complexity of previously known algorithms for the general problem, but also for algorithms devised for special cases. For the case when the objective is weighted absolute deviation, Sokkalingam et al. (1999) devised an algorithm with run time O(n 2 m log(nC)) for C the maximum edge weight. For the sum of absolute deviations our algorithm runs in time O(n 2 log n), matching the run time of a recent (Ahuja and Orlin 2000) improvement for this case. A new algorithm for bipartite matching in path graphs is reported here with complexity of O(n 1.5 log n). This leads to a second algorithm for the sum of absolute deviations running in O(n 1.5 log n log C) steps.

FAST CLUSTERING AND MINIMUM WEIGHT MATCHING ALGORITHMS FOR VERY LARGE MOBILE BACKBONE WIRELESS NETWORKS

Mobile Backbone Wireless Networks (MBWN) [10] are wireless networks in which the base stations are mobile. Our strategy is the following: mobile nodes are dynamically grouped into clusters of bounded radius. In the very large wireless networks we deal with we deal with, several hundreds of clusters may be generated. Clustering makes use of a two dimensional Euclidean version of the Antipole Tree data structure [5]. This very effective structure was originally designed for finite sets of points in an arbitrary metric space to support efficient range searching. It requires only a linear number of pair-wise distance calculations among nodes. Mobile Base Stations occupy an approximate centroid of the clusters and are moved according to a fast practical bipartite matching algorithm which tries to minimize both total and maximum distance. We show that the best known computational geometry algorithms [1] become infeasible for our application when a high number of mobile base stations is required. On the other hand our proposed 8% average error solution requires O (k log k) running time instead of the approximatively O (k2) exact algorithm [1]. Communication among nodes is realized by a Clusterhead Gateway Switching Routing (CGSR) protocol [15] where the mobile base stations are organized in a suitable network. Other efficient clustering algorithms [11, 17] may be used instead of the Antipole Tree. However the nice hierarchical structure of the Antipole Tree makes it applicable to other types of mobile wireless (Ad-Hoc) and wired networks but this will be subject of future work.

An Optimization Based Approach to the Train Operator Scheduling Problem at Singapore MRT

Singapore Mass Rapid Transit (SMRT) operates two train lines with 83 kilometers of track and 48 stations. A total of 77 trains are in operation during peak hours and 41 during off-peak hours. In this article we report on an optimization based approach to develop a computerized train-operator scheduling system that has been implemented at SMRT. The approach involves a bipartite matching algorithm for the generation of night duties and a tabu search algorithm for the generation of day duties. The system automates the train-operator scheduling process at SMRT and produces favorable schedules in comparison with the manual process. It is also able to handle the multiple objectives inherent in the crew scheduling system. While trying to minimize the system wide crew-related costs, the system is also able to address concern with respect to the number of split duties.

On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix

We consider bipartite matching algorithms for computing permutations of a sparse matrix so that the diagonal of the permuted matrix has entries of large absolute value. We discuss various strategies for this and consider their implementation as computer codes. We also consider scaling techniques to further increase the relative values of the diagonal entries. Numerical experiments show the effect of the reorderings and the scaling on the solution of sparse equations by a direct method and by preconditioned iterative techniques.

One and Two Facility Network Design Revisited

The one facility one commodity network design problem (OFOC) with nonnegative flow costs considers the problem of sending d units of flow from a source to a destination where arc capacity is purchased in batches of C units. The two facility problem (TFOC) is similar, but capacity can be purchased either in batches of C units or one unit. Flow costs are zero. These problems are known to be NP-hard. We describe an exact O(n33 n ) algorithm for these problems based on the repeated use of a bipartite matching algorithm. We also present a better lower bound of Ω(n2k*) for an earlier Ω(n2k) algorithm described in the literature where k=⌊d/C⌋ and k*=min k,⌊(n−2)/2⌋. The matching algorithm is faster than this one for k≥⌊(n−2)/2⌋. Finally, we provide another reformulation of the problem that is quasi integral. This property could be useful in designing a modified version of the simplex method to solve the problem using a sequence of pivots with integer extreme solutions, referred to as the integral simplex method in the literature.