How Good Are Popular Matchings?

In this paper, we consider the Hospital Residents problem (HR) and the Hospital Residents problem with Lower Quotas (HRLQ). In this model with two sided preferences, stability is a well accepted notion of optimality. However, in the presence of lower quotas, a stable and feasible matching need not exist. For the HRLQ problem, our goal therefore is to output a good feasible matching assuming that a feasible matching exists. Computing matchings with minimum number of blocking pairs (Min-BP) and minimum number of blocking residents (Min-BR) are known to be NP-Complete. The only approximation algorithms for these problems work under severe restrictions on the preference lists. We present an algorithm which circumvents this restriction and computes a popular matching in the HRLQ instance. We show that on data-sets generated using various generators, our algorithm performs very well in terms of blocking pairs and blocking residents. Yokoi [Yokoi, 2017] recently studied envy-free matchings for the HRLQ problem. We propose a simple modification to Yokoi\u27s algorithm to output a maximal envy-free matching. We observe that popular matchings outperform envy-free matchings on several parameters of practical importance, like size, number of blocking pairs, number of blocking residents. In the absence of lower quotas, that is, in the Hospital Residents (HR) problem, stable matchings are guaranteed to exist. Even in this case, we show that popularity is a practical alternative to stability. For instance, on synthetic data-sets generated using a particular model, as well as on real world data-sets, a popular matching is on an average 8-10% larger in size, matches more number of residents to their top-choice, and more residents prefer the popular matching as compared to a stable matching. Our comprehensive study reveals the practical appeal of popular matchings for the HR and HRLQ problems. To the best of our knowledge, this is the first study on the empirical evaluation of popular matchings in this setting

Scalable Robust Kidney Exchange

In barter exchanges, participants directly trade their endowed goods in a constrained economic setting without money. Transactions in barter exchanges are often facilitated via a central clearinghouse that must match participants even in the face of uncertainty---over participants, existence and quality of potential trades, and so on. Leveraging robust combinatorial optimization techniques, we address uncertainty in kidney exchange, a real-world barter market where patients swap (in)compatible paired donors. We provide two scalable robust methods to handle two distinct types of uncertainty in kidney exchange---over the quality and the existence of a potential match. The latter case directly addresses a weakness in all stochastic-optimization-based methods to the kidney exchange clearing problem, which all necessarily require explicit estimates of the probability of a transaction existing---a still-unsolved problem in this nascent market. We also propose a novel, scalable kidney exchange formulation that eliminates the need for an exponential-time constraint generation process in competing formulations, maintains provable optimality, and serves as a subsolver for our robust approach. For each type of uncertainty we demonstrate the benefits of robustness on real data from a large, fielded kidney exchange in the United States. We conclude by drawing parallels between robustness and notions of fairness in the kidney exchange setting.Comment: Presented at AAAI1

Tight Bounds for Randomized Load Balancing on Arbitrary Network Topologies

We consider the problem of balancing load items (tokens) in networks. Starting with an arbitrary load distribution, we allow nodes to exchange tokens with their neighbors in each round. The goal is to achieve a distribution where all nodes have nearly the same number of tokens. For the continuous case where tokens are arbitrarily divisible, most load balancing schemes correspond to Markov chains, whose convergence is fairly well-understood in terms of their spectral gap. However, in many applications, load items cannot be divided arbitrarily, and we need to deal with the discrete case where the load is composed of indivisible tokens. This discretization entails a non-linear behavior due to its rounding errors, which makes this analysis much harder than in the continuous case. We investigate several randomized protocols for different communication models in the discrete case. As our main result, we prove that for any regular network in the matching model, all nodes have the same load up to an additive constant in (asymptotically) the same number of rounds as required in the continuous case. This generalizes and tightens the previous best result, which only holds for expander graphs, and demonstrates that there is almost no difference between the discrete and continuous cases. Our results also provide a positive answer to the question of how well discrete load balancing can be approximated by (continuous) Markov chains, which has been posed by many researchers.Comment: 74 pages, 4 figure

Visual SLAM using straight lines

The present thesis is focuses on the problem of Simultaneous Localisation and Mapping (SLAM) using only visual data (VSLAM). This means to concurrently estimate the position of a moving camera and to create a consistent map of the environment. Since implementing a whole VSLAM system is out of the scope of a degree thesis, the main aim is to improve an existing visual SLAM system by complementing the commonly used point features with straight line primitives. This enables more accurate localization in environments with few feature points, like corridors. As a foundation for the project, ScaViSLAM by Strasdat et al. is used, which is a state-of-the-art real-time visual SLAM framework. Since it currently only supports Stereo and RGB-D systems, implementing a Monocular approach will be researched as well as an integration of it as a ROS package in order to deploy it on a mobile robot. For the experimental results, the Care-O-bot service robot developed by Fraunhofer IPA will be used

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Exploratory search through large video corpora

Activity retrieval is a growing field in electrical engineering that specializes in the search and retrieval of relevant activities and events in video corpora. With the affordability and popularity of cameras for government, personal and retail use, the quantity of available video data is rapidly outscaling our ability to reason over it. Towards the end of empowering users to navigate and interact with the contents of these video corpora, we propose a framework for exploratory search that emphasizes activity structure and search space reduction over complex feature representations. Exploratory search is a user driven process wherein a person provides a system with a query describing the activity, event, or object he is interested in finding. Typically, this description takes the implicit form of one or more exemplar videos, but it can also involve an explicit description. The system returns candidate matches, followed by query refinement and iteration. System performance is judged by the run-time of the system and the precision/recall curve of of the query matches returned. Scaling is one of the primary challenges in video search. From vast web-video archives like youtube (1 billion videos and counting) to the 30 million active surveillance cameras shooting an estimated 4 billion hours of footage every week in the United States, trying to find a set of matches can be like looking for a needle in a haystack. Our goal is to create an efficient archival representation of video corpora that can be calculated in real-time as video streams in, and then enables a user to quickly get a set of results that match. First, we design a system for rapidly identifying simple queries in large-scale video corpora. Instead of focusing on feature design, our system focuses on the spatiotemporal relationships between those features as a means of disambiguating an activity of interest from background. We define a semantic feature vocabulary of concepts that are both readily extracted from video and easily understood by an operator. As data streams in, features are hashed to an inverted index and retrieved in constant time after the system is presented with a user's query. We take a zero-shot approach to exploratory search: the user manually assembles vocabulary elements like color, speed, size and type into a graph. Given that information, we perform an initial downsampling of the archived data, and design a novel dynamic programming approach based on genome-sequencing to search for similar patterns. Experimental results indicate that this approach outperforms other methods for detecting activities in surveillance video datasets. Second, we address the problem of representing complex activities that take place over long spans of space and time. Subgraph and graph matching methods have seen limited use in exploratory search because both problems are provably NP-hard. In this work, we render these problems computationally tractable by identifying the maximally discriminative spanning tree (MDST), and using dynamic programming to optimally reduce the archive data based on a custom algorithm for tree-matching in attributed relational graphs. We demonstrate the efficacy of this approach on popular surveillance video datasets in several modalities. Finally, we design an approach for successive search space reduction in subgraph matching problems. Given a query graph and archival data, our algorithm iteratively selects spanning trees from the query graph that optimize the expected search space reduction at each step until the archive converges. We use this approach to efficiently reason over video surveillance datasets, simulated data, as well as large graphs of protein data