搜索结果：Matching

Let $G = (A \cup B, E)$ be an instance of the stable marriage problem with strict preference lists. A matching $M$ is popular in $G$ if $M$ does not lose a head-to-head election against any matching where vertices are voters. Every stable matching is a min-size popular matching; another subclass of popular matchings that always exist and can be easily computed is the set of dominant matchings. A popular matching $M$ is dominant if $M$ wins the head-to-head election against any larger matching. Thus every dominant matching is a max-size popular matching and it is known that the set of dominant matchings is the linear image of the set of stable matchings in an auxiliary graph. Results from the literature seem to suggest that stable and dominant matchings behave, from a complexity theory point of view, in a very similar manner within the class of popular matchings. The goal of this paper is to show that indeed there are differences in the tractability of stable and dominant matchings, and to investigate further their importance for popular matchings. First, we show that it is easy to check if all popular matchings are also stable, however it is co-NP hard to check if all popular match

We introduce a new two-sided stable matching problem that describes the summer internship matching practice of an Australian university. The model is a case between two models of Kamada and Kojima on matchings with distributional constraints. We study three solution concepts, the strong and weak stability concepts proposed by Kamada and Kojima, and a new one in between the two, called cutoff stability. Kamada and Kojima showed that a strongly stable matching may not exist in their most restricted model with disjoint regional quotas. Our first result is that checking its existence is NP-hard. We then show that a cutoff stable matching exists not just for the summer internship problem but also for the general matching model with arbitrary heredity constraints. We present an algorithm to compute a cutoff stable matching and show that it runs in polynomial time in our special case of summer internship model. However, we also show that finding a maximum size cutoff stable matching is NP-hard, but we provide a Mixed Integer Linear Program formulation for this optimisation problem.

We study the stable matching problem in non-bipartite graphs with incomplete but strict preference lists, where the edges have weights and the goal is to compute a stable matching of minimum or maximum weight. This problem is known to be NP-hard in general. Our contribution is two fold: a polyhedral characterization and an approximation algorithm. Previously Chen et al. have shown that the stable matching polytope is integral if and only if the subgraph obtained after running phase one of Irving's algorithm is bipartite. We improve upon this result by showing that there are instances where this subgraph might not be bipartite but one can further eliminate some edges and arrive at a bipartite subgraph. Our elimination procedure ensures that the set of stable matchings remains the same, and thus the stable matching polytope of the final subgraph contains the incidence vectors of all stable matchings of our original graph. This allows us to characterize a larger class of instances for which the weighted stable matching problem is polynomial-time solvable. We also show that our edge elimination procedure is best possible, meaning that if the subgraph we arrive at is not bipartite, then

Schema matching is a foundational task in enterprise data integration, aiming to align disparate data sources. While traditional methods handle simple one-to-one table mappings, they often struggle with complex multi-table schema matching in real-world applications. We present LLMatch, a unified and modular schema matching framework. LLMatch decomposes schema matching into three distinct stages: schema preparation, table-candidate selection, and column-level alignment, enabling component-level evaluation and future-proof compatibility. It includes a novel two-stage optimization strategy: a Rollup module that consolidates semantically related columns into higher-order concepts, followed by a Drilldown module that re-expands these concepts for fine-grained column mapping. To address the scarcity of complex semantic matching benchmarks, we introduce SchemaNet, a benchmark derived from real-world schema pairs across three enterprise domains, designed to capture the challenges of multi-table schema alignment in practical settings. Experiments demonstrate that LLMatch significantly improves matching accuracy in complex schema matching settings and substantially boosts engineer productivi

The palindrome pattern matching (pal-matching) is a kind of generalized pattern matching, in which two strings $x$ and $y$ of same length are considered to match (pal-match) if they have the same palindromic structures, i.e., for any possible $1 \le i < j \le |x| = |y|$, $x[i..j]$ is a palindrome if and only if $y[i..j]$ is a palindrome. The pal-matching problem is the problem of searching for, in a text, the occurrences of the substrings that pal-match with a pattern. Given a text $T$ of length $n$ over an alphabet of size $σ$, an index for pal-matching is to support, given a pattern $P$ of length $m$, the counting queries that compute the number $\mathsf{occ}$ of occurrences of $P$ and the locating queries that compute the occurrences of $P$. The authors in~[I et al., Theor. Comput. Sci., 2013] proposed an $O(n \lg n)$-bit data structure to support the counting queries in $O(m \lg σ)$ time and the locating queries in $O(m \lg σ+ \mathsf{occ})$ time. In this paper, we propose an FM-index type index for the pal-matching problem, which we call the PalFM-index, that occupies $2n \lg \min(σ, \lg n) + 2n + o(n)$ bits of space and supports the counting queries in $O(m)$ time. The Pal

Local feature matching is challenging due to textureless and repetitive patterns. Existing methods focus on using appearance features and global interaction and matching, while the importance of geometry priors in local feature matching has not been fully exploited. Different from these methods, in this paper, we delve into the importance of geometry prior and propose Structured Epipolar Matcher (SEM) for local feature matching, which can leverage the geometric information in an iterative matching way. The proposed model enjoys several merits. First, our proposed Structured Feature Extractor can model the relative positional relationship between pixels and high-confidence anchor points. Second, our proposed Epipolar Attention and Matching can filter out irrelevant areas by utilizing the epipolar constraint. Extensive experimental results on five standard benchmarks demonstrate the superior performance of our SEM compared to state-of-the-art methods. Project page: https://sem2023.github.io.

Dataset distillation aims to synthesize small datasets with little information loss from original large-scale ones for reducing storage and training costs. Recent state-of-the-art methods mainly constrain the sample synthesis process by matching synthetic images and the original ones regarding gradients, embedding distributions, or training trajectories. Although there are various matching objectives, currently the strategy for selecting original images is limited to naive random sampling. We argue that random sampling overlooks the evenness of the selected sample distribution, which may result in noisy or biased matching targets. Besides, the sample diversity is also not constrained by random sampling. These factors together lead to optimization instability in the distilling process and degrade the training efficiency. Accordingly, we propose a novel matching strategy named as \textbf{D}ataset distillation by \textbf{RE}present\textbf{A}tive \textbf{M}atching (DREAM), where only representative original images are selected for matching. DREAM is able to be easily plugged into popular dataset distillation frameworks and reduce the distilling iterations by more than 8 times without p

A novel image matching method is proposed that utilizes learned features extracted by an off-the-shelf deep neural network to obtain a promising performance. The proposed method uses pre-trained VGG architecture as a feature extractor and does not require any additional training specific to improve matching. Inspired by well-established concepts in the psychology area, such as the Mental Rotation paradigm, an initial warping is performed as a result of a preliminary geometric transformation estimate. These estimates are simply based on dense matching of nearest neighbors at the terminal layer of VGG network outputs of the images to be matched. After this initial alignment, the same approach is repeated again between reference and aligned images in a hierarchical manner to reach a good localization and matching performance. Our algorithm achieves 0.57 and 0.80 overall scores in terms of Mean Matching Accuracy (MMA) for 1 pixel and 2 pixels thresholds respectively on Hpatches dataset, which indicates a better performance than the state-of-the-art.

The approximate string matching is a fundamental and recurrent problem that arises in most computer science fields. This problem can be defined as follows: Let $D=\{x_1,x_2,\ldots x_d\}$ be a set of $d$ words defined on an alphabet $Σ$, let $q$ be a query defined also on $Σ$, and let $k$ be a positive integer. We want to build a data structure on $D$ capable of answering the following query: find all words in $D$ that are at most different from the query word $q$ with $k$ errors. In this thesis, we study the approximate string matching methods in dictionaries, texts, and indexes, to propose practical methods that solve this problem efficiently. We explore this problem in three complementary directions: 1) The approximate string matching in the dictionary. We propose two solutions to this problem, the first one uses hash tables for $k \geq 2$, the second uses the Trie and reverse Trie, and it is restricted to (k = 1). The two solutions are adaptable, without loss of performance, to the approximate string matching in a text. 2) The approximate string matching for \textit{autocompletion}, which is, find all suffixes of a given prefix that may contain errors. We give a new solution bet

This paper aims to interpret how deepfake detection models learn artifact features of images when just supervised by binary labels. To this end, three hypotheses from the perspective of image matching are proposed as follows. 1. Deepfake detection models indicate real/fake images based on visual concepts that are neither source-relevant nor target-relevant, that is, considering such visual concepts as artifact-relevant. 2. Besides the supervision of binary labels, deepfake detection models implicitly learn artifact-relevant visual concepts through the FST-Matching (i.e. the matching fake, source, target images) in the training set. 3. Implicitly learned artifact visual concepts through the FST-Matching in the raw training set are vulnerable to video compression. In experiments, the above hypotheses are verified among various DNNs. Furthermore, based on this understanding, we propose the FST-Matching Deepfake Detection Model to boost the performance of forgery detection on compressed videos. Experiment results show that our method achieves great performance, especially on highly-compressed (e.g. c40) videos.

Stereo matching is close to hitting a half-century of history, yet witnessed a rapid evolution in the last decade thanks to deep learning. While previous surveys in the late 2010s covered the first stage of this revolution, the last five years of research brought further ground-breaking advancements to the field. This paper aims to fill this gap in a two-fold manner: first, we offer an in-depth examination of the latest developments in deep stereo matching, focusing on the pioneering architectural designs and groundbreaking paradigms that have redefined the field in the 2020s; second, we present a thorough analysis of the critical challenges that have emerged alongside these advances, providing a comprehensive taxonomy of these issues and exploring the state-of-the-art techniques proposed to address them. By reviewing both the architectural innovations and the key challenges, we offer a holistic view of deep stereo matching and highlight the specific areas that require further investigation. To accompany this survey, we maintain a regularly updated project page that catalogs papers on deep stereo matching in our Awesome-Deep-Stereo-Matching (https://github.com/fabiotosi92/Awesome-D

We present a novel approximate graph matching algorithm that incorporates seeded data into the graph matching paradigm. Our Joint Optimization of Fidelity and Commensurability (JOFC) algorithm embeds two graphs into a common Euclidean space where the matching inference task can be performed. Through real and simulated data examples, we demonstrate the versatility of our algorithm in matching graphs with various characteristics--weightedness, directedness, loopiness, many-to-one and many-to-many matchings, and soft seedings.

Local feature matching enjoys wide-ranging applications in the realm of computer vision, encompassing domains such as image retrieval, 3D reconstruction, and object recognition. However, challenges persist in improving the accuracy and robustness of matching due to factors like viewpoint and lighting variations. In recent years, the introduction of deep learning models has sparked widespread exploration into local feature matching techniques. The objective of this endeavor is to furnish a comprehensive overview of local feature matching methods. These methods are categorized into two key segments based on the presence of detectors. The Detector-based category encompasses models inclusive of Detect-then-Describe, Joint Detection and Description, Describe-then-Detect, as well as Graph Based techniques. In contrast, the Detector-free category comprises CNN Based, Transformer Based, and Patch Based methods. Our study extends beyond methodological analysis, incorporating evaluations of prevalent datasets and metrics to facilitate a quantitative comparison of state-of-the-art techniques. The paper also explores the practical application of local feature matching in diverse domains such a

This paper studies masked autoencoder (MAE) video pre-training for various temporal matching-based downstream tasks, i.e., object-level tracking tasks including video object tracking (VOT) and video object segmentation (VOS), self-supervised visual correspondence learning, dense tracking tasks including optical flow estimation and long-term point tracking, and 3D point cloud tracking. Specifically, our work explores to provide a general representation to boost the temporal matching ability in various downstream tracking tasks. To achieve this, we firstly find that a simple extension of MAE, which randomly masks out frame patches in videos and reconstruct the frame pixels, heavily relies on spatial cues while ignoring temporal relations for frame reconstruction, thus leading to sub-optimal temporal matching representations. To alleviate this, we propose DropMAE, which adaptively performs spatial-attention dropout in the frame reconstruction to facilitate temporal correspondence learning in videos. We obtain several important findings with DropMAE: 1) DropMAE is a strong and efficient temporal matching learner, which achieves better fine-tuning results on matching-based tasks than th

We apply the Darmois and the $C^3$ matching conditions to three different spherically symmetric spacetimes. The exterior spacetime is described by the Schwarzschild vacuum solution whereas for the interior counterpart we choose different perfect fluid solutions with the same symmetry. We show that Darmois matching conditions are satisfied in all three cases whereas the $C^3$ conditions are not fulfilled. We argue that this difference is due to a non-physical behavior of the pressure on the matching surface.

We propose a model for online graph problems where algorithms are given access to an oracle that predicts (e.g., based on modeling assumptions or on past data) the degrees of nodes in the graph. Within this model, we study the classic problem of online bipartite matching, and a natural greedy matching algorithm called MinPredictedDegree, which uses predictions of the degrees of offline nodes. For the bipartite version of a stochastic graph model due to Chung, Lu, and Vu where the expected values of the offline degrees are known and used as predictions, we show that MinPredictedDegree stochastically dominates any other online algorithm, i.e., it is optimal for graphs drawn from this model. Since the "symmetric" version of the model, where all online nodes are identical, is a special case of the well-studied "known i.i.d. model", it follows that the competitive ratio of MinPredictedDegree on such inputs is at least 0.7299. For the special case of graphs with power law degree distributions, we show that MinPredictedDegree frequently produces matchings almost as large as the true maximum matching on such graphs. We complement these results with an extensive empirical evaluation showing

The matching formulation makes it naturally hard for the stereo matching to handle ill-posed regions like occlusions and non-Lambertian surfaces. Fusing monocular priors has been proven helpful for ill-posed matching, but the biased monocular prior learned from small stereo datasets constrains the generalization. Recently, stereo matching has progressed by leveraging the unbiased monocular prior from the vision foundation model (VFM) to improve the generalization in ill-posed regions. We dive into the fusion process and observe three main problems limiting the fusion of the VFM monocular prior. The first problem is the misalignment between affine-invariant relative monocular depth and absolute depth of disparity. Besides, when we use the monocular feature in an iterative update structure, the over-confidence in the disparity update leads to local optima results. A direct fusion of a monocular depth map could alleviate the local optima problem, but noisy disparity results computed at the first several iterations will misguide the fusion. In this paper, we propose a binary local ordering map to guide the fusion, which converts the depth map into a binary relative format, unifying the

We present simulation-free score and flow matching ([SF]$^2$M), a simulation-free objective for inferring stochastic dynamics given unpaired samples drawn from arbitrary source and target distributions. Our method generalizes both the score-matching loss used in the training of diffusion models and the recently proposed flow matching loss used in the training of continuous normalizing flows. [SF]$^2$M interprets continuous-time stochastic generative modeling as a Schrödinger bridge problem. It relies on static entropy-regularized optimal transport, or a minibatch approximation, to efficiently learn the SB without simulating the learned stochastic process. We find that [SF]$^2$M is more efficient and gives more accurate solutions to the SB problem than simulation-based methods from prior work. Finally, we apply [SF]$^2$M to the problem of learning cell dynamics from snapshot data. Notably, [SF]$^2$M is the first method to accurately model cell dynamics in high dimensions and can recover known gene regulatory networks from simulated data. Our code is available in the TorchCFM package at https://github.com/atong01/conditional-flow-matching.

Ontology matching is defined as finding a relationship or correspondence between two or more entities in two or more ontologies. To solve the interoperability problem of the domain ontologies, semantically similar entities in these ontologies must be found and aligned before merging them. GraphMatcher, developed in this study, is an ontology matching system using a graph attention approach to compute higher-level representation of a class together with its surrounding terms. The GraphMatcher has obtained remarkable results in in the Ontology Alignment Evaluation Initiative (OAEI) 2022 conference track. Its codes are available at ~\url{https://github.com/sefeoglu/gat_ontology_matching}.

We introduce the visual acoustic matching task, in which an audio clip is transformed to sound like it was recorded in a target environment. Given an image of the target environment and a waveform for the source audio, the goal is to re-synthesize the audio to match the target room acoustics as suggested by its visible geometry and materials. To address this novel task, we propose a cross-modal transformer model that uses audio-visual attention to inject visual properties into the audio and generate realistic audio output. In addition, we devise a self-supervised training objective that can learn acoustic matching from in-the-wild Web videos, despite their lack of acoustically mismatched audio. We demonstrate that our approach successfully translates human speech to a variety of real-world environments depicted in images, outperforming both traditional acoustic matching and more heavily supervised baselines.