Multiobject tracking as maximum weight independent set

Maximum weight independent set for [formula omitted]claw-free graphs in polynomial time

We present improved results for approximating maximum-weight independent set (MaxIS) in the CONGEST and LOCAL models of distributed computing. Given an input graph, let n and Δ be the number of nodes and maximum degree, respectively, and let MIS(n,Δ) be the running time of finding a maximal independent set (MIS) in the CONGEST model. Bar-Yehuda et al. [PODC 2017] showed that there is an algorithm in the CONGEST model that finds a Δ-approximation for MaxIS in O(MIS(n,Δ)log W) rounds, where W is the maximum weight of a node in the graph, which can be as large as poly (n). Whether their algorithm is deterministic or randomized that succeeds with high probability depends on the MIS algorithm that is used as a black-box. Our results: 1) A deterministic O(MIS(n,Δ)/e)-round algorithm that finds a (1+e)Δ-approximation for MaxIS in the CONGEST model. 2) A randomized (poly(log log n)/e)-round algorithm that finds, with high probability, a (1+e)Δ-approximation for MaxIS in the CONGEST model. That is, by sacrificing only a tiny fraction of the approximation guarantee, we achieve an exponential speed-up in the running time over the previous best known result. 3) A randomized O(log n⋅ poly(log log n)/e)-round algorithm that finds, with high probability, a 8(1+e)α-approximation for MaxIS in the CONGEST model, where α is the arboricity of the graph. For graphs of arboricity α < Δ/(8(1+e)), this result improves upon the previous best known result in both the approximation factor and the running time. One may wonder whether it is possible to approximate MaxIS with high probability in fewer than poly(log log n) rounds. Interestingly, a folklore randomized ranking algorithm by Boppana implies a single round algorithm that gives an expected Δ-approximation in the CONGEST model. However, it is unclear how to convert this algorithm to one that succeeds with high probability without sacrificing a large number of rounds. For unweighted graphs of maximum degree Δ ≤ n/log n, we show a new analysis of the randomized ranking algorithm, which we combine with the local-ratio technique, to provide a O(1/e)-round algorithm in the CONGEST model that, with high probability, finds an independent set of size at least n/((1+e)(Δ+1)). This result cannot be extended to very high degree graphs, as we show a lower bound of Ω(log^*n) rounds for any randomized algorithm that with probability at least 1-1/log n finds an independent set of size Ω(n/Δ). This lower bound holds even for the LOCAL model. The hard instances that we use to prove our lower bound are graphs of maximum degree Δ = Ω(n/log^*n).

To solve the low accuracy and poor stability in traditional object tracking methods for martial arts competition videos, a Kalman filtering algorithm based on feature matching and multi object tracking is proposed for object detection in martial arts competition videos. Firstly, feature matching in multi target tracking is studied. Then, based on target feature matching, the Kalman filtering algorithm is fused to construct a target detection model in martial arts videos. Finally, simulation experiments are conducted to verify the performance and application effectiveness of the model. The results showed that the average tracking errors of the model on the X and Y axes were 3.86% and 3.38%, respectively. At the same time, the average accuracy and recall rate in the video target tracking process were 93.64% and 95.48%, respectively. After 100 iterations, the results gradually stabilized. This indicated that the constructed model could accurately detect targets in martial arts competition videos. It had high tracking accuracy and robustness. Compared with traditional object detection methods, this algorithm has better performance and effectiveness. The Kalman filter algorithm based on feature matching and multi target tracking has broad application prospects and research value in target detection in martial arts competition videos.

The vertices in many graphs are weighted unequally in real scenarios, but the previous studies on the maximum independent set (MIS) ignore the weights of vertices. Therefore, the weight of an MIS may not necessarily be the largest. In this paper, we study the problem of maximum weighted independent set (MWIS) that is defined as the set of independent vertices with the largest weight. Since it is intractable to deliver the exact solution for large graphs, we design a reducing and tie-breaking framework to compute a near-maximum weighted independent set. The reduction rules are critical to reduce the search space for both exact and greedy algorithms as they determine the vertices that are definitely (or not) in the MWIS while preserving the correctness of solutions. We devise a set of novel reductions including low-degree reductions and high-degree reductions for general weighted graphs. Extensive experimental studies over real graphs confirm that our proposed method outperforms the state-of-the-arts significantly in terms of both effectiveness and efficiency.

Three fast algorithms have been developed to solve the problem of data association in multitarget tracking in clutter. In the first algorithm, the problem of data association is identified as an exhaustive search problem in general. Subsequently, a mathematical model is proposed for the problem of data association in the joint probabilistic data association filter (JPDAF). Based on the model, a depth-first search (DFS) approach is developed for the fast generation of data association hypotheses and the computation of the conditional probabilities of the hypotheses in the JPDAF. When the density of targets is moderate, a second algorithm is developed to directly compute a posteriori probabilities in the JPDAF without generating the data association hypotheses. In the third algorithm, the effect of interference due to closely spaced targets is simplified. An approach to approximately compute the a posteriori probabilities in the JPDAF is developed. The computational complexity of the algorithms is analyzed in the worst case, as well as in the average case.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Maximum weight independent sets in hole- and dart-free graphs

We study the maximum weight independent sets of links between nodes distributed randomly in an infinite plane. Different definitions of the weight of a link are considered, leading to slight variations of what is essentially a spatial reuse problem in wireless multihop networks. A simple interference model is assumed with the interference radius equaling the transmission radius. In addition to unidirectional interference from a transmitter to the receivers of other links, also an RTS/CTS-type bidirectional handshake is considered. We study both the case where the transmission radius is fixed and tunable through power control. With a fixed transmission radius, we derive asymptotic results for the low- and high-density regimes. The main contribution is in the numerical results for the maximum weight, establishing some previously unknown parameters of stochastic geometry. The results are obtained by the Moving Window Algorithm that is able to find the maximum weight independent set in a strip of limited height but unlimited length. By studying the results as a function of the height of the strip, we are able to extrapolate to the infinite plane.

An LP-based algorithm for the data association problem in multitarget tracking

RNA secondary structures are vital in determining the 3-D structures of noncoding RNA molecules, which in turn affect their functions. Computational RNA secondary structure alignment and analysis are biologically significant, because they help identify numerous functionally important motifs. Unfortunately, many analysis methods suffer from computational intractability in the presence of pseudoknots. The conversion of knotted to knot-free secondary structures is an essential preprocessing step, and is regarded as pseudoknot removal. Although exact methods have been proposed for this task, their computational complexities are undetermined, and so their efficiencies in processing complex pseudoknots are currently unknown. We transformed the pseudoknot removal problem into a circle graph maximum weight independent set (MWIS) problem, in which each MWIS represents a unique optimal deknotted structure. An existing circle graph MWIS algorithm was extended to report either single or all solutions. Its time complexity depends on the number of MWISs, and is guaranteed to report one solution in polynomial time. Experimental results suggest that our extended algorithm is much more efficient than the state-of-the-art tool. We also devised a novel concept called the structural scoring function, and investigated its effectiveness in more accurate solution candidate selection for a certain criteria.

This paper presents a cluster head selection algorithm in wireless network, which is based on an optimal algorithm to find a maximum weighted independent set (MWIS) in planar graph. It is analysed that the wireless AD hoc networks and the application of the maximum weighted independent set. To prove the validity and practicability of MWIS, we compare MWIS algorithm with minimum ID clustering algorithm and maximum degree clustering algorithm by using a topological subgraph.

The central problem in multitarget/multisensor tracking is the data association problem of partitioning the observations into tracks and false alarms so that an accurate estimate of the true tracks can be recovered. This data association problem is formulated in this work as a multidimensional assignment problem. These NP-hard data association problems are large scale, have noisy objective functions, and must be solved in real-time. A class of Lagrangian relaxation algorithms has been developed to construct near-optimal solutions in real-time, and thus the purpose of this work is to demonstrate many of the salient features of tracking problems by using these algorithms to numerically investigate constant acceleration models observed by a radar in two dimensional space. This formulation includes gating, clustering, and optimization problems associated with filtering. Extensive numerical simulations are used to demonstrate the effectiveness and robustness of a class of Lagrangian relaxation algorithms for the solution of these problems to the noise level in the problems.

We present a (1+ε)-approximation algorithm with quasi-polynomial running time for computing a maximum weight independent set of polygons from a given set of polygons in the plane. Contrasting this, the best-known polynomial time algorithm for the problem has an approximation ratio of n ε . Surprisingly, we can extend the algorithm to the problem of computing the maximum cardinality subset of the given set of polygons whose intersection graph fulfills some sparsity condition. For example, we show that one can approximate the maximum subset of polygons such that the intersection graph of the subset is planar or does not contain a cycle of length 4 (i.e., K 2,2 ). Our algorithm relies on a recursive partitioning scheme, whose backbone is the existence of balanced cuts with small complexity that intersect polygons from the optimal solution of a small total weight. For the case of large axis-parallel rectangles, we provide a polynomial time (1 + ε)-approximation for the maximum weight independent set. Specifically, we consider the problem where each rectangle has one edge whose length is at least a constant fraction of the length of the corresponding edge of the bounding box of all the input elements. This is now the most general case for which a PTAS is known, and it requires a new and involved partitioning scheme, which should be of independent interest.

Real-time object detection and tracking in video streams has become a fundamental component of modern intelligent systems, enabling applications in surveillance, autonomous driving, robotics, healthcare monitoring, and smart cities. The rapid advancement of deep learning techniques has significantly improved the accuracy and efficiency of detecting and tracking multiple objects under complex and dynamic environments. This study presents a deep learning–based framework for real-time object detection and tracking in continuous video streams, emphasizing both computational efficiency and detection robustness.The proposed system integrates a state-of-the-art convolutional neural network (CNN)-based object detector with a reliable multi-object tracking algorithm. The detection module identifies objects of interest in each frame, while the tracking component maintains consistent identities across consecutive frames by utilizing motion prediction and feature association strategies. To achieve real-time performance, the model is optimized through lightweight network architectures and parallel processing on GPU hardware. Data augmentation and transfer learning techniques are employed to enhance generalization and reduce training time. Performance evaluation is conducted on benchmark video datasets using standard metrics such as precision, recall, mean Average Precision (mAP), and tracking accuracy. Experimental results demonstrate that the proposed framework achieves high detection accuracy while maintaining low latency, making it suitable for real-time deployment. Furthermore, the system effectively handles challenges such as occlusion, scale variation, and illumination changes. This research presents a comprehensive study on real-time object detection and tracking in video streams using deep learning techniques. The proposed framework integrates YOLO-based object detection with Deep SORT multi-object tracking to achieve robust spatial localization and temporal identity preservation. The study evaluates performance using benchmark datasets including COCO, MOT17, and KITTI. Mathematical formulations of detection loss, Kalman filtering, and data association are presented. Experimental analysis using precision, recall, mAP, MOTA, ROC-AUC, and PR-AUC demonstrates that the system achieves high detection accuracy while maintaining real-time performance above 35 frames per second. The findings confirm that deep learning-based frameworks provide scalable and efficient solutions for surveillance, autonomous vehicles, and intelligent monitoring systems.

Occlusion, a pervasive challenge in Multi-Object Tracking (MOT) within complex scenes, severely degrades tracking performance. Current methods still face numerous problems when handling occlusions. Motion prediction struggles to accommodate diverse motion patterns, resulting in failure during short-term occlusions. Concurrently, appearance features possess insufficient discriminative power under occluded conditions, which frequently leads to identity switches following long-term occlusion. To enhance the performance of MOT under such challenging conditions, we propose an innovative Occlusion-Aware Multi-Object Tracking via Joint Diffusion Motion Prediction and Appearance Purification (OAMOT). For short-term occlusions, a Diffusion Motion Recovery Model (DMRM) is developed, which integrates residual and noise diffusion branches to recover trajectories precisely under varied motion patterns. For long-term occlusions, the SAM Appearance Purification for ReID (SAPR) module is proposed; the module leverages the mask generation mechanism of SAM as foreground attention to enhance feature discriminability. Furthermore, a Lightweight Attention Predictor (LAP) is integrated into the ReID network to achieve SAM-quality attention during inference without significant computational overhead. Experimental results on the MOT17, MOT20, and DanceTrack datasets demonstrate that the proposed OAMOT method outperforms current state-of-the-art multi-object tracking techniques across multiple evaluation metrics. The code can be available on https://github.com/wangtuo111/OAMOT.

Object detection and tracking is one of the most important and challenging branches in computer vision, and have been widely applied in various fields, such as health-care monitoring, autonomous driving, anomaly detection, and so on. With the rapid development of deep learning (DL) networks and GPU’s computing power, the performance of object detectors and trackers has been greatly improved. To understand the main development status of object detection and tracking pipeline thoroughly, in this survey, we have critically analyzed the existing DL network-based methods of object detection and tracking and described various benchmark datasets. This includes the recent development in granulated DL models. Primarily, we have provided a comprehensive overview of a variety of both generic object detection and specific object detection models. We have enlisted various comparative results for obtaining the best detector, tracker, and their combination. Moreover, we have listed the traditional and new applications of object detection and tracking showing its developmental trends. Finally, challenging issues, including the relevance of granular computing, in the said domain are elaborated as a future scope of research, together with some concerns. An extensive bibliography is also provided.