Compatibility Graph Research Articles

On Generalizations of Pairwise Compatibility Graphs

A graph $G$ is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree and an interval $I$, such that each leaf of the tree is a vertex of the graph, and there is an edge $\{ x, y \}$ in $G$ if and only if the weight of the path in the tree connecting $x$ and $y$ lies within the interval $I$. Originating in phylogenetics, PCGs are closely connected to important graph classes like leaf-powers and multi-threshold graphs, widely applied in bioinformatics, especially in understanding evolutionary processes. In this paper we introduce two natural generalizations of the PCG class, namely $k$-OR-PCG and $k$-AND-PCG, which are the classes of graphs that can be expressed as union and intersection, respectively, of $k$ PCGs. These classes can be also described using the concepts of the covering number and the intersection dimension of a graph in relation to the PCG class. We investigate how the classes of OR-PCG and AND-PCG are related to PCGs, $k$-interval-PCGs and other graph classes known in the literature. In particular, we provide upper bounds on the minimum $k$ for which an arbitrary graph $G$ belongs to $k$-interval-PCGs, $k$-OR-PCG or $k$-AND-PCG classes. For particular graph classes we improve these general bounds. Moreover, we show that, for every integer $k$, there exists a bipartite graph that is not in the $k$-interval-PCGs class, proving that there is no finite $k$ for which the $k$-interval-PCG class contains all the graphs. This answers an open question of Ahmed and Rahman from 2017. Finally, using a Ramsey theory argument, we show that for any $k$, there exists graphs that are not in $k$-AND-PCG, and graphs that are not in $k$-OR-PCG.

MAC: Maximal Cliques for 3D Registration.

This paper presents a 3D registration method with maximal cliques (MAC) for 3D point cloud registration (PCR). The key insight is to loosen the previous maximum clique constraint and mine more local consensus information in a graph for accurate pose hypotheses generation: 1) A compatibility graph is constructed to render the affinity relationship between initial correspondences. 2) We search for maximal cliques in the graph, each representing a consensus set. 3) Transformation hypotheses are computed for the selected cliques by the SVD algorithm and the best hypothesis is used to perform registration. In addition, we present a variant of MAC if given overlap prior, called MAC-OP. Overlap prior further enhances MAC from many technical aspects, such as graph construction with re-weighted nodes, hypotheses generation from cliques with additional constraints, and hypothesis evaluation with overlap-aware weights. Extensive experiments demonstrate that both MAC and MAC-OP effectively increase registration recall, outperform various state-of-the-art methods, and boost the performance of deep-learned methods. For instance, MAC combined with GeoTransformer achieves a state-of-the-art registration recall of 95.7% / 78.9% on 3DMatch / 3DLoMatch. We perform synthetic experiments on 3DMatch-LIR / 3DLoMatch-LIR, a dataset with extremely low inlier ratios for 3D registration in ultra-challenging cases. Code will be available at: https://github.com/zhangxy0517/3D-Registration-with-Maximal-Cliques.

Performance paradox of dynamic matching models under greedy policies

We consider the stochastic matching model on a non-bipartite compatibility graph and analyze the impact of adding an edge to the expected number of items in the system. One may see adding an edge as increasing the flexibility of the system, for example, asking a family registering for social housing to list fewer requirements in order to be compatible with more housing units. Therefore, it may be natural to think that adding edges to the compatibility graph will lead to a decrease in the expected number of items in the system and the waiting time to be assigned. In our previous work, we proved this is not always true for the First Come First Matched discipline and provided sufficient conditions for the existence of the performance paradox: despite a new edge in the compatibility graph, the expected total number of items can increase. These sufficient conditions are related to the heavy-traffic assumptions in queueing systems. The intuition behind this is that the performance paradox occurs when the added edge in the compatibility graph disrupts the draining of a bottleneck. In this paper, we generalize this performance paradox result to a family of so-called greedy matching policies and explore the type of compatibility graphs where such a paradox occurs. Intuitively, a greedy matching policy never leaves compatible items unassigned, so the state space of the system consists of finite words of item classes that belong to an independent set of the compatibility graph. Some examples of greedy matching policies are First Come First Match, Match the Longest, Match the Shortest, Random, Priority. We prove several results about the existence of performance paradoxes for greedy disciplines for some family of graphs. More precisely, we prove several results about the lifting of the paradox from one graph to another one. For a certain family of graphs, we prove that there exists a paradox for the whole family of greedy policies. Most of these results are based on strong aggregation of Markov chains and graph theoretical properties.

Fast Robust Point Cloud Registration Based on Compatibility Graph and Accelerated Guided Sampling

Point cloud registration is a crucial technique in photogrammetry, remote sensing, etc. A generalized 3D point cloud registration framework has been developed to estimate the optimal rigid transformation between two point clouds using 3D key point correspondences. However, challenges arise due to the uncertainty in 3D key point detection techniques and the similarity of local surface features. These factors often lead to feature descriptors establishing correspondences containing significant outliers. Current point cloud registration algorithms are typically hindered by these outliers, affecting both their efficiency and accuracy. In this paper, we propose a fast and robust point cloud registration method based on a compatibility graph and accelerated guided sampling. By constructing a compatible graph with correspondences, a minimum subset sampling method combining compatible edge sampling and compatible vertex sampling is proposed to reduce the influence of outliers on the estimation of the registration parameters. Additionally, an accelerated guided sampling strategy based on preference scores is presented, which effectively utilizes model parameters generated during the iterative process to guide the sampling toward inliers, thereby enhancing computational efficiency and the probability of estimating optimal parameters. Experiments are carried out on both synthetic and real-world data. The experimental results demonstrate that our proposed algorithm achieves a significant balance between registration accuracy and efficiency compared to state-of-the-art registration algorithms such as RANSIC and GROR. Even with up to 2000 initial correspondences and an outlier ratio of 99%, our algorithm achieves a minimum rotation error of 0.737° and a minimum translation error of 0.0201 m, completing the registration process within 1 s.

Traffic Waiting Time Optimization: An Effective Effort to Overcome Congestion at Gede Ngurah Cakranegara Intersection

Intersections are places that are prone to traffic congestion. This is due to the location and function of the intersection, which if left unchecked will lead to accidents. To overcome this problem, traffic lights are made to regulate traffic flow conditions. Gede Ngurah Cakranegara Intersection is an intersection that has high congestion conditions, this is due to its location in the city center and its function as a main road. In addition, the trigger for congestion at the Gede Ngurah Cakranegara intersection is the waiting time which is still not optimal and the lack of orderly drivers in obeying the traffic lights. Thus, the purpose of this study is to optimize the total waiting time at the Gede Ngurah Cakranegara intersection. Total waiting time optimization is done using compatible graph. The compatible graph in this case will describe the condition of traffic flows that will run simultaneously without interfering with each other, so that they are safe and do not collide with each other. This study uses primary data obtained from field observations conducted in the morning, afternoon and evening. After optimization, the total waiting time at the Gede Ngurah Cakranegara intersection following the light signal is 180 seconds and the total waiting time for those who do not follow the light signal is 120 seconds. Compared to the previous waiting time of 538 seconds, a more optimal time was obtained.

Semi-Supervised Multiview Feature Selection With Adaptive Graph Learning.

As data sources become ever more numerous with increased feature dimensionality, feature selection for multiview data has become an important technique in machine learning. Semi-supervised multiview feature selection (SMFS) focuses on the problem of how to obtain a discriminative feature subset from heterogeneous feature spaces in the case of abundant unlabeled data with little labeled data. Most existing methods suffer from unreliable similarity graph structure across different views since they separate the graph construction from feature selection and use the fixed graphs that are susceptible to noisy features. Furthermore, they directly concatenate multiple feature projections for feature selection, neglecting the contribution diversity among projections. To alleviate these problems, we present an SMFS to simultaneously select informative features and learn a unified graph through the data fusion from aspects of feature projection and similarity graph. Specifically, SMFS adaptively weights different feature projections and flexibly fuses them to form a joint weighted projection, preserving the complementarity and consensus of the original views. Moreover, an implicit graph fusion is devised to dynamically learn a compatible graph across views according to the similarity structure in the learned projection subspace, where the undesirable effects of noisy features are largely alleviated. A convergent method is derived to iteratively optimize SMFS. Experiments on various datasets validate the effectiveness and superiority of SMFS over state-of-the-art methods.

Application of Compatible Graph and Webster Methods for Traffic Light Arrangement in Jepara

The problem of congestion has become a common problem that is often found on the highways, especially at the crossroads, without exception in Jepara Regency. The Mayong-Jepara Highway intersection is classified as a busy intersection that is full of vehicles during every departure and return hours, which are dominated by factory employees. Congestion often occurs at these intersections even though there are traffic lights that regulate the movement of vehicles. So, This study aims to find the solutions to congestion problems at Mayong-Jepara Highway intersection through compatible graph modeling and optimizing traffic light cycle time using the Webster method. Compatible graphs are used to determine traffic flows that are worked to move simultaneously without causing collisions, and that are used to carry out the graph weighting to determine the number of phases. The variables used in this applied research are the data on the number of vehicles, road width, and traffic light duration that taken directly in the field. Because the traffic density in the morning and afternoon is different for each intersection arm. Thus, the cycle time is determined in 2 sessions namely the morning and the afternoon. From the modeling of the compatible graph that has been weighted, it is obtained that the morning and afternoon sessions have 3 phases as the total which are then used to determine the traffic light cycle time. As a result, the cycle times for the morning session are 98 seconds, and the afternoon session is 155 seconds. The results were then simulated with PTV Vissim software and assessed to be quite effective in dealing with congestion and heavy traffic at the Mayong-Jepara Highway intersection especially in the afternoon session.

Spectral Geometric Verification: Re-Ranking Point Cloud Retrieval for Metric Localization

In large-scale metric localization, an incorrect result during retrieval will lead to an incorrect pose estimate or loop closure. Re-ranking methods propose to take into account all the top retrieval candidates and re-order them to increase the likelihood of the top candidate being correct. However, state-of-the-art re-ranking methods are inefficient when re-ranking many potential candidates due to their need for resource intensive point cloud registration between the query and each candidate. In this work, we propose an efficient spectral method for geometric verification (named SpectralGV) that does not require registration. We demonstrate how the optimal inter-cluster score of the correspondence compatibility graph of two point clouds represents a robust fitness score measuring their spatial consistency. This score takes into account the subtle geometric differences between structurally similar point clouds and therefore can be used to identify the correct candidate among potential matches retrieved by global similarity search. SpectralGV is deterministic, robust to outlier correspondences, and can be computed in parallel for all potential candidates. We conduct extensive experiments on 5 large-scale datasets to demonstrate that SpectralGV outperforms other state-of-the-art re-ranking methods and show that it consistently improves the recall and pose estimation of 3 state-of-the-art metric localization architectures while having a negligible effect on their runtime. The open-source implementation and trained models are available at: https://github.com/csiro-robotics/SpectralGV.

Half-cycle: A new formulation for modelling kidney exchange problems

We introduce the half-cycle formulation (HCF), a new integer programming (IP) model for the kidney exchange problem, which has life-saving applications. In HCF, a cycle (i.e., set of kidney swaps) is represented by two compatible halves. After giving several algorithmic enhancements for HCF, we show through extensive computational experiments with an IP solver that our new model outperforms existing formulations when the cycle size limit is set to 4, 5, or 6, depending on the density of the compatibility graph.

PERBANDINGAN PENERAPAN GRAF KOMPATIBEL DENGAN REALITA DILAPANGAN DALAM PENGATURAN LAMPU LALU LINTAS PERSIMPANGAN BANDARA PEKANBARU

To minimize traffic congestion, the application of compatible graphs is used to establish a more optimal total waiting duration at the traffic flow at the Pekanbaru airport intersection. Traffic flow at the Pekanbaru airport intersection is more congested on Sunday due to weekends, where this study was conducted on Sunday afternoon, May 29, 2022. The purpose is to optimize the total waiting duration of the existing traffic lights in the area, waiting for the vehicle stop time obtained in all aspects of the lane, from the observations that have been made obtained compatible graphs. By applying compatible graphs, two different hypotheses are used. The first hypothesis turns left following a traffic light which is 100 seconds. Meanwhile, the second hypothesis of turning left does not follow a traffic light of 120 seconds. Where the wait duration obtained is the optimum waiting duration with a compatible graph, the waiting duration in the current field is much more optimal than the waiting time after using the compatible graph

Coordinated flight path planning for a fleet of missiles in high-risk areas

AbstractThis paper addresses the flight path planning problem for multiple missiles engaging stationary targets in high-risk areas. Targets protected by air defence are preferably engaged by a fleet or swarm of missiles, not individual missiles. The concept of a swarm attack is that a large number of approaching missiles overwhelm air defence. The deployment of missiles is often part of a broader mission including further participants. Flight path planning is then an integral element of mission planning, requiring strict timing coordination of all members involved. The flight times of the missiles are dictated by the master planning. We present algorithms for offline planning and online re-planning of flight paths for a fleet of missiles with flight time constraints. The algorithms are based on an advanced bidirectional RRT* algorithm that generates risk-minimizing flight paths with predefined flight times. Online planning generates the flight paths of the fleet sequentially, maintaining a safety distance between the missiles to prevent mutual collision. Offline planning uses a global optimization approach to determine an optimal selection of flight paths from a large set of potential paths. The selection is performed by a branch and bound algorithm that determines optimal cliques in the path compatibility graph. The optimization is embedded in an iterative algorithm that allows to successively improve the mission success.

The Adjacency Matrix of The Compatible Action Graph for Finite Cyclic Groups of p-Power Order

Let G and H be two finites -groups, then is the non-abelian tensor product of G and H. In this paper, the compatible action graph for has been considered when and for the two finite -groups by determining the adjacency matrix for and studied some of its properties.

Modeling of Traffic Flow Schemes at Road Intersections in Pekanbaru City Using Compatible Graphs

Congestion is one of the few issues that has always been the center of attention at crossroads. One of them is at the intersection of Tuanku Tambusai, Nangka and Soekarno Hatta road. This congestion can be reduced by optimizing the duration of pauses at road intersections and collecting a compatible traffic flow when a red light occurs. The two traffic flows are said to be compatible if the two flows are running together without anyone crashing. A compatible graph is a graph that has two sets in which the object to be arranged is indicated by its points, and the corresponding pair of objects is indicated by its sides. This study obtained the optimal pause duration, which assumes a left turn following a red light for 75 seconds, by applying a compatible graph. Furthermore, the optimal duration of the pause assumes that the left turn does not follow the red light for 45 seconds. The pause duration is smaller than the duration now used on Soekarno Hatta Road, which is 115 seconds, using the assumption of following the red light to turn left. So obtained, the duration of the pause is much more optimal when compared to the duration of the pause used on the current Soekarno Hatta road

Genetically compatible graphs for planetary gear train synthesis

Planetary gear trains (PGTs) are used in a wide range of mechanical applications. Graphs are used to represent PGTs. PGTs are classified into single-planet and multi-planet gear trains depending on the number of vertices in the second level of the graph. In this paper, a novel method for synthesizing PGTs up to the second level is developed. The first step in the synthesis process is the enumeration of spanning trees. A combinatorial analysis is then used to obtain the link assortment arrays and categorize them into families. Based on the parent graphs and spanning trees, the geared graphs are generated for each family. For simplicity, the steps of the newly developed genetically compatible graphing method are applied to 5-link, 1-DOF planetary gear trains. The synthesis steps are programmed in MATLAB.

New results on pairwise compatibility graphs

A graph G=(V,E) is called a pairwise compatibility graph (PCG) if there exists an edge-weighted tree T and two non-negative real numbers dmin and dmax such that each leaf u of T corresponds to a vertex u∈V and there is an edge (u,v)∈E if and only if dmin≤dT(u,v)≤dmax, where dT(u,v) is the sum of the weights of the edges on the unique path from u to v in T. The tree T is called the pairwise compatibility tree (PCT) of G. It has been proven that not all graphs are PCGs. Thus, it is interesting to know which classes of graphs are PCGs. In this paper, we prove that grid graphs are PCGs. Although there are a necessary condition and a sufficient condition known for a graph being a PCG, there are some classes of graphs that are intermediate to the classes defined by the necessary condition and the sufficient condition. In this paper, we show two examples of graphs that are included in these intermediate classes and prove that they are not PCGs.

UAV-based MEC-assisted automated traffic management scheme using blockchain

In this paper, an automated real-time traffic management scheme is proposed by using unmanned aerial vehicles (UAV) in an effective and secured way. However, owing to the low computational capability and limited battery capacity of a UAV, multi-access edge computing (MEC) is applied to enhance the performance of an automated UAV-based traffic management scheme. Additionally, blockchain technology is introduced in the automated traffic management scheme to store the traffic record for providing network repudiation and avoiding any third-party interference with the network. An algorithm is developed based on the concept of a pairwise compatibility graph for the UAV-assisted automated traffic management scheme wherein a deep learning (DL) model is used for vehicle detection. Moreover, a two-phase authentication mechanism is proposed for a faster and secure verification process of the registered devices in the proposed scheme. Finally, a result analysis is conducted based on the security analysis and performance analysis to verify the effectiveness of the proposed scheme.

Load Balancing Under Strict Compatibility Constraints

Consider a system with N identical single-server queues and a number of task types, where each server is able to process only a small subset of possible task types. Arriving tasks select [Formula: see text] random compatible servers and join the shortest queue among them. The compatibility constraints are captured by a fixed bipartite graph between the servers and the task types. When the graph is complete bipartite, the mean-field approximation is accurate. However, such dense compatibility graphs are infeasible for large-scale implementation. We characterize a class of sparse compatibility graphs for which the mean-field approximation remains valid. For this, we introduce a novel notion, called proportional sparsity, and establish that systems with proportionally sparse compatibility graphs asymptotically match the performance of a fully flexible system. Furthermore, we show that proportionally sparse random compatibility graphs can be constructed, which reduce the server degree almost by a factor [Formula: see text] compared with the complete bipartite compatibility graph. Funding: This work was supported by the National Science Foundation [Grant CCF-2113027].

Genetically compatible graphs for planetary gear train synthesis

Reinforced concrete, RC beams subjected to shear failure which is the most unwanted failure mode due to speed progress is studied numerically. Therefore, the effective design of beams is necessary because of the sudden failure types of these beams in shear. The minimum shear reinforcement ratio of RC beams must be provided around the longitudinal rebars. Thus, the stirrups with different patterns have a significant benefit for improving the RC beam. In this paper, the performance of specimens with different spiral stirrups using ANSYS programs is investigated by comparing them with conventional stirrups of RC beams. One statement on the experimental results has been obtained from previous research Karayannis et al. [17]. The behaviors of these experimental beams are compared with finite element analysis of the identical beams. It is found that the behaviors of the experimental beam in comparison with the behaviors of the numerical beam are slightly different. Based on the FE analysis, the shear strength results demonstrated the mean accuracy and standard deviation of about 0.994 and 0.028, respectively, compared with the experimental test. Furthermore, the curve determined from FE analysis is consistent with the experiment data. The results give knowledge about the importance of spiral stirrups of the beam, and the most effective method among the investigated cases.

Flexibility can Hurt Dynamic Matching System Performance

We study the performance of stochastic matching models with general compatibility graphs. Items of different classes arrive to the system according to independent Poisson processes. Upon arrival, an item is matched with a compatible item according to the First Come First Matched discipline and both items leave the system immediately. If there are no compatible items, the new arrival joins the queue of unmatched items of the same class. Compatibilities between item classes are defined by a connected graph, where nodes represent the classes of items and the edges the compatibilities between item classes. We show that such a model may exhibit a non intuitive behavior: increasing the matching flexibility by adding new edges in the matching graph may lead to a larger average population at the steady state. This performance paradox can be viewed as an analog of the Braess paradox. We show sufficient conditions for the existence or non-existence of this paradox. This performance paradox in matching models appears when specific independent sets are in saturation, i.e., the system is close to the stability condition.

Unified Multiple Constant Multipliers for Dynamic Exchange of Low-Precision Kernels on FPGAs

Recent work has shown that small, fast, and power-efficient multiple constant multiplication (MCM) implementations can be realized on FPGAs rather than requiring specialized embedded multipliers. However, the limited silicon area on FPGAs requires applications such as image processing to frequently exchange the multiplier (filter) blocks in a series of filtering operations, and no previous works have considered the MCM problem under topological constraint to avoid time-consuming partial reconfiguration on FPGAs. In this paper, we define a unified MCM (UMCM) problem of finding a unified hardware topology for the multiplier blocks frequently exchanged and introduce a framework termed compatible graph synthesis to solve the problem efficiently. Using a set of parameters to logarithmic shifters, dynamic exchange of multiplier blocks with the unified topology can be realized without partial reconfiguration on FPGAs. Experimental results show that the solution is valuable for applications that require frequent exchange of multiplier blocks on FPGAs due to a limited silicon area budget.