arXiv subjects

Martin Aleksandrov

Publications and source records attributed to Martin Aleksandrov.

15 recordsLinked to original sources

arXiv2023

TReR: A Lightweight Transformer Re-Ranking Approach for 3D LiDAR Place Recognition

Autonomous driving systems often require reliable loop closure detection to guarantee reduced localization drift. Recently, 3D LiDAR-based localization methods have used retrieval-based place recognition to find revisited places efficiently. However, when deployed in challenging real-world scenarios, the place recognition models become more complex, which comes at the cost of high computational demand. This work tackles this problem from an information-retrieval perspective, adopting a first-retrieve-then-re-ranking paradigm, where an initial loop candidate ranking, generated from a 3D place recognition model, is re-ordered by a proposed lightweight transformer-based re-ranking approach (TReR). The proposed approach relies on global descriptors only, being agnostic to the place recognition model. The experimental evaluation, conducted on the KITTI Odometry dataset, where we compared TReR with s.o.t.a. re-ranking approaches such as alphaQE and SGV, indicate the robustness and efficiency when compared to alphaQE while offering a good trade-off between robustness and efficiency when compared to SGV.

cs.CV↗

arXiv2020

Two Algorithms for Additive and Fair Division of Mixed Manna

We consider a fair division model in which agents have positive, zero and negative utilities for items. For this model, we analyse one existing fairness property - EFX - and three new and related properties - EFX$_0$, EFX$^3$ and EF1$^3$ - in combination with Pareto-optimality. With general utilities, we give a modified version of an existing algorithm for computing an EF1$^3$ allocation. With $-α/0/α$ utilities, this algorithm returns an EFX$^3$ and PO allocation. With absolute identical utilities, we give a new algorithm for an EFX and PO allocation. With $-α/0/β$ utilities, this algorithm also returns such an allocation. We report some new impossibility results as well.

cs.GT↗

arXiv2020

Monotone and Online Fair Division

We study a new but simple model for online fair division in which indivisible items arrive one-by-one and agents have monotone utilities over bundles of the items. We consider axiomatic properties of mechanisms for this model such as strategy-proofness, envy-freeness, and Pareto efficiency. We prove a number of impossibility results that justify why we consider relaxations of the properties, as well as why we consider restricted preference domains on which good axiomatic properties can be achieved. We propose two mechanisms that have good axiomatic fairness properties on restricted but common preference domains.

cs.GT↗

arXiv2020

Group Envy Freeness and Group Pareto Efficiency in Fair Division with Indivisible Items

We study the fair division of items to agents supposing that agents can form groups. We thus give natural generalizations of popular concepts such as envy-freeness and Pareto efficiency to groups of fixed sizes. Group envy-freeness requires that no group envies another group. Group Pareto efficiency requires that no group can be made better off without another group be made worse off. We study these new group properties from an axiomatic viewpoint. We thus propose new fairness taxonomies that generalize existing taxonomies. We further study near versions of these group properties as allocations for some of them may not exist. We finally give three prices of group fairness between group properties for three common social welfares (i.e. utilitarian, egalitarian, and Nash).

cs.GT↗

arXiv2020

Strategy-proofness, Envy-freeness and Pareto efficiency in Online Fair Division with Additive Utilities

We consider fair division problems where indivisible items arrive one-by-one in an online fashion and are allocated immediately to agents who have additive utilities over these items. Many existing offline mechanisms do not work in this online setting. In addition, many existing axiomatic results often do not transfer from the offline to the online setting. For this reason, we propose here three new online mechanisms, as well as consider the axiomatic properties of three previously proposed online mechanisms. In this paper, we use these mechanisms and characterize classes of online mechanisms that are strategy-proof, and return envy-free and Pareto efficient allocations, as well as combinations of these properties. Finally, we identify an important impossibility result.

cs.GT↗

arXiv2020

Expected Outcomes and Manipulations in Online Fair Division

Two simple and attractive mechanisms for the fair division of indivisible goods in an online setting are LIKE and BALANCED LIKE. We study some fundamental computational problems concerning the outcomes of these mechanisms. In particular, we consider what expected outcomes are possible, what outcomes are necessary, and how to compute their exact outcomes. In general, we show that such questions are more tractable to compute for LIKE than for BALANCED LIKE. As LIKE is strategy-proof but BALANCED LIKE is not, we also consider the computational problem of how, with BALANCED LIKE, an agent can compute a strategic bid to improve their outcome. We prove that this problem is intractable in general.

cs.GT↗

arXiv2020

Most Competitive Mechanisms in Online Fair Division

This paper combines two key ingredients for online algorithms - competitive analysis (e.g. the competitive ratio) and advice complexity (e.g. the number of advice bits needed to improve online decisions) - in the context of a simple online fair division model where items arrive one by one and are allocated to agents via some mechanism. We consider four such online mechanisms: the popular Ranking matching mechanism adapted from online bipartite matching and the Like, Balanced Like and Maximum Like allocation mechanisms firstly introduced for online fair division problems. Our first contribution is that we perform a competitive analysis of these mechanisms with respect to the expected size of the matching, the utilitarian welfare, and the egalitarian welfare. We also suppose that an oracle can give a number of advice bits to the mechanisms. Our second contribution is to give several impossibility results; e.g. no mechanism can achieve the egalitarian outcome of the optimal offline mechanism supposing they receive partial advice from the oracle. Our third contribution is that we quantify the competitive performance of these four mechanisms w.r.t. the number of oracle requests they can make. We thus present a most-competitive mechanism for each objective.

cs.GT↗

arXiv2020

Envy-freeness up to one item: Shall we add or remove resources?

We consider a fair division model in which agents have general valuations for bundles of indivisible items. We propose two new axiomatic properties for allocations in this model: EF1+- and EFX+-. We compare these with the existing EF1 and EFX. Although EF1 and EF1+- allocations often exist, our results assert eloquently that EFX+- and PO allocations exist in each case where EFX and PO allocations do not exist. Additionally, we prove several new impossibility and incompatibility results.

cs.GT↗

arXiv2020

Jealousy-freeness and other common properties in Fair Division of Mixed Manna

We consider a fair division setting where indivisible items are allocated to agents. Each agent in the setting has strictly negative, zero or strictly positive utility for each item. We, thus, make a distinction between items that are good for some agents and bad for other agents (i.e. mixed), good for everyone (i.e. goods) or bad for everyone (i.e. bads). For this model, we study axiomatic concepts of allocations such as jealousy-freeness up to one item, envy-freeness up to one item and Pareto-optimality. We obtain many new possibility and impossibility results in regard to combinations of these properties. We also investigate new computational tasks related to such combinations. Thus, we advance the state-of-the-art in fair division of mixed manna.

cs.GT↗

arXiv2019

Greedy Algorithms for Fair Division of Mixed Manna

We consider a multi-agent model for fair division of mixed manna (i.e. items for which agents can have positive, zero or negative utilities), in which agents have additive utilities for bundles of items. For this model, we give several general impossibility results and special possibility results for three common fairness concepts (i.e. EF1, EFX, EFX3) and one popular efficiency concept (i.e. PO). We also study how these interact with common welfare objectives such as the Nash, disutility Nash and egalitarian welfares. For example, we show that maximizing the Nash welfare with mixed manna (or minimizing the disutility Nash welfare) does not ensure an EF1 allocation whereas with goods and the Nash welfare it does. We also prove that an EFX3 allocation may not exist even with identical utilities. By comparison, with tertiary utilities, EFX and PO allocations, or EFX3 and PO allocations always exist. Also, with identical utilities, EFX and PO allocations always exist. For these cases, we give polynomial-time algorithms, returning such allocations and approximating further the Nash, disutility Nash and egalitarian welfares in special cases.

cs.AI↗

arXiv2019

Online Fair Division: A Survey

We survey a burgeoning and promising new research area that considers the online nature of many practical fair division problems. We identify wide variety of such online fair division problems, as well as discuss new mechanisms and normative properties that apply to this online setting. The online nature of such fair division problems provides both opportunities and challenges such as the possibility to develop new online mechanisms as well as the difficulty of dealing with an uncertain future.

cs.AI↗

arXiv2018

Fair Division Minimizing Inequality

Behavioural economists have shown that people are often averse to inequality and will make choices to avoid unequal outcomes. In this paper, we consider how to allocate indivisible goods fairly so as to minimize inequality. We consider how this interacts with axiomatic properties such as envy-freeness, Pareto efficiency and strategy-proofness. We also consider the computational complexity of computing allocations minimizing inequality. Unfortunately, this is computationally intractable in general so we consider several tractable greedy online mechanisms that minimize inequality. Finally, we run experiments to explore the performance of these methods.

cs.GT↗

arXiv2018

Almost Envy Freeness and Welfare Efficiency in Fair Division with Goods or Bads

We consider two models of fair division with indivisible items: one for goods and one for bads. For goods, we study two generalized envy freeness proxies (EF1 and EFX for goods) and three common welfare (utilitarian, egalitarian and Nash) efficiency notions. For bads, we study two generalized envy freeness proxies (1EF and XEF for goods) and two less common diswelfare (egalitarian and Nash) efficiency notions. Some existing algorithms for goods do not work for bads. We thus propose several new algorithms for the model with bads. Our new algorithms exhibit many nice properties. For example, with additive identical valuations, an allocation that maximizes the egalitarian diswelfare or Nash diswelfare is XEF and PE. Finally, we also give simple and tractable cases when these envy freeness proxies and welfare efficiency are attainable in combination (e.g. binary valuations, house allocations).

cs.GT↗

arXiv2017

Sustainable Fair Division

In this paper, I summarize our work on online fair division. In particular, I present two models for online fair division: (1) one existing model for fair division in food banks and (2) one new model for fair division of deceased organs to patients. I further discuss simple mechanisms for these models that allocate the resources as they arrive to agents. In practice, agents are often risk-averse having imperfect information. Within this assumption, I report several interesting axiomatic and complexity results for these mechanisms and conclude with future work.

cs.GT↗

arXiv2015

Online Fair Division: analysing a Food Bank problem

We study an online model of fair division designed to capture features of a real world charity problem. We consider two simple mechanisms for this model in which agents simply declare what items they like. We analyse several axiomatic properties of these mechanisms like strategy-proofness and envy-freeness. Finally, we perform a competitive analysis and compute the price of anarchy.

cs.GT↗