Approximately EFX Allocations for Indivisible Chores

In this paper, we study how to fairly allocate a set of m indivisible chores to a group of n agents, each of which has a general additive cost function on the items. Since envy-free (EF) allocations are not guaranteed to exist, we consider the notion of envy-freeness up to any item (EFX). In contrast to the fruitful results regarding the (approximation of) EFX allocations for goods, very little is known for the allocation of chores. Prior to our work, for the allocation of chores, it is known that EFX allocations always exist for two agents or general number of agents with identical ordering cost functions. For general instances, no non-trivial approximation result regarding EFX allocation is known. In this paper, we make progress in this direction by providing several polynomial time algorithms for the computation of EFX and approximately EFX allocations. We show that for three agents we can always compute a 4.45-approximation of EFX allocation. For n>=4 agents, our algorithm always computes a (3n^2-n)-approximation. We also study the bi-valued instances, in which agents have at most two cost values on the chores. For three agents, we provide an algorithm for the computation of EFX allocations. For n>=4 agents, we present algorithms for the computation of partial EFX allocations with at most n-1 unallocated items; and (n-1)-approximation of EFX allocations.Comment: Include new results about partial EFX allocations and improved results regarding approximate EFX allocation

Multi-agent Online Scheduling: MMS Allocations for Indivisible Items

We consider the problem of fairly allocating a sequence of indivisible items that arrive online in an arbitrary order to a group of n agents with additive normalized valuation functions. We consider both the allocation of goods and chores and propose algorithms for approximating maximin share (MMS) allocations. When agents have identical valuation functions the problem coincides with the semi-online machine covering problem (when items are goods) and load balancing problem (when items are chores), for both of which optimal competitive ratios have been achieved. In this paper, we consider the case when agents have general additive valuation functions. For the allocation of goods, we show that no competitive algorithm exists even when there are only three agents and propose an optimal 0.5-competitive algorithm for the case of two agents. For the allocation of chores, we propose a (2-1/n)-competitive algorithm for n>=3 agents and a square root of 2 (approximately 1.414)-competitive algorithm for two agents. Additionally, we show that no algorithm can do better than 15/11 (approximately 1.364)-competitive for two agents.Comment: 29 pages, 1 figure (to appear in ICML 2023

Improved Competitive Ratios for Online Bipartite Matching on Degree Bounded Graphs

We consider the online bipartite matching problem on $(k,d)$-bounded graphs, where each online vertex has at most $d$ neighbors, each offline vertex has at least $k$ neighbors, and $k\geq d\geq 2$. The model of $(k,d)$-bounded graphs is proposed by Naor and Wajc (EC 2015 and TEAC 2018) to model the online advertising applications in which offline advertisers are interested in a large number of ad slots, while each online ad slot is interesting to a small number of advertisers. They proposed deterministic and randomized algorithms with a competitive ratio of $1 - (1-1/d)^k$ for the problem, and show that the competitive ratio is optimal for deterministic algorithms. They also raised the open questions of whether strictly better competitive ratios can be achieved using randomized algorithms, for both the adversarial and stochastic arrival models. In this paper we answer both of their open problems affirmatively. For the adversarial arrival model, we propose a randomized algorithm with competitive ratio $1 - (1-1/d)^k + \Omega(d^{-4}\cdot e^{-\frac{k}{d}})$ for all $k\geq d\geq 2$. We also consider the stochastic model and show that even better competitive ratios can be achieved. We show that for all $k\geq d\geq 2$, the competitive ratio is always at least $0.8237$. We further consider the $b$-matching problem when each offline vertex can be matched at most $b$ times, and provide several competitive ratio lower bounds for the adversarial and stochastic model.Comment: 23 pages, 5 figure

Improved Competitive Ratio for Edge-Weighted Online Stochastic Matching

We consider the edge-weighted online stochastic matching problem, in which an edge-weighted bipartite graph G=(I\cup J, E) with offline vertices J and online vertex types I is given. The online vertices have types sampled from I with probability proportional to the arrival rates of online vertex types. The online algorithm must make immediate and irrevocable matching decisions with the objective of maximizing the total weight of the matching. For the problem with general arrival rates, Feldman et al. (FOCS 2009) proposed the Suggested Matching algorithm and showed that it achieves a competitive ratio of 1-1/e \approx 0.632. The ratio has recently been improved to 0.645 by Yan (2022), who proposed the Multistage Suggested Matching (MSM) algorithm. In this paper, we propose the Evolving Suggested Matching (ESM) algorithm, and show that it achieves a competitive ratio of 0.650.Comment: To appear in WINE202

AxWin Transformer: A Context-Aware Vision Transformer Backbone with Axial Windows

Recently Transformer has shown good performance in several vision tasks due to its powerful modeling capabilities. To reduce the quadratic complexity caused by the attention, some outstanding work restricts attention to local regions or extends axial interactions. However, these methos often lack the interaction of local and global information, balancing coarse and fine-grained information. To address this problem, we propose AxWin Attention, which models context information in both local windows and axial views. Based on the AxWin Attention, we develop a context-aware vision transformer backbone, named AxWin Transformer, which outperforming the state-of-the-art methods in both classification and downstream segmentation and detection tasks

Disability-Free Life Expectancy among People Over 60 Years Old by Sex, Urban and Rural Areas in Jiangxi Province, China

Objective: To estimate and compare age trends and the disability-free life expectancy (DFLE) of the population over 60 years old in 2018 in Jiangxi Province, China, by sex and urban–rural areas. Methods: The model life table was employed to estimate the age-specific mortality rate by sex and urban–rural areas, based on the Summary of Health Statistics of Jiangxi Province in 2018 and the Sixth National Health Service survey of Jiangxi Province. DFLE and its ratio to life expectancy (LE) were obtained by the Sullivan method. Results: In 2018, the DFLE among people over 60 is 17.157 years for men and is 19.055 years for women, accounting for 89.7% and 86.5% of their LE respectively. The DFLE/LE of men is higher than that of women at all ages. LE and DFLE are higher for the population in urban areas than in rural areas. For women, DFLE/LE is higher in urban areas than in rural areas (except at ages 75 and 80). Urban men have a higher DFLE/LE than rural men (except at age 85). The difference in DFLE between men and women over 60 years is 1.898 years, of which 2.260 years are attributable to the mortality rate, and 0.362 years are due to the disability-free prevalence. In addition, the difference in DFLE between urban–rural elderly over 60 years old is mostly attributed to the mortality rate by gender (male: 0.902/1.637; female: 0.893/1.454), but the impact of the disability-free rate cannot be ignored either (male: 0.735/1.637; female: 0.561/1.454). Conclusions: The increase in DFLE is accompanied by the increase in LE, but with increased age, DFLE/LE gradually decreases. With advancing age, the effect of disability on elderly people becomes more severe. The government administration must implement some preventive actions to improve health awareness and the life quality of the elderly. Rural elderly; rural women in particular, need to be paid more attention and acquire more health care

Experimental validation of a quasi-realtime human respiration detection method via UWB radar

In this paper, we propose a quasi-realtime human respiration detection method via UWB radar system in through-wall or similar condition. With respect to the previous proposed automatic detection method, the new proposed method assures competitive performance in the human respiration motion detection and effective noise/clutter rejection, which have been proved by experimental results in actual scenario. This new method has also been implemented in a UWB through-wall life-detection radar prototype, and its time consuming is about 2 s, which can satisfy the practical requirement of quasi-realtime for through-wall sequential vital sign detection. Therefore, it can be an alternative for through-obstacles static human detection in antiterrorism or rescue scenarios

A Modified Specific Fuel Consumption Analysis for Predicting the Rearrangement of Energy System Structures

AbstractOne variation of exergy analysis, specific fuel consumption (SFC) analysis, was modified according the advanced exergy analysis, where exergy destructions within each component were split into endogenous/exogenous and avoidable/unavoidable parts, and by combining the energy-savings effects of each component. The modified analysis approach can help locate not only the weak points at the component level but also certain bottlenecks from the topology viewpoint, which may indicate adding or deleting some components, or enhancing the thermodynamic interactions between different process or subsystems. The modified approach was then applied to a conventional coal-fired power plant. The detailed spatial distribution of SFC within the current system at different partial-load conditions were deeply discussed at both component and process levels. Further splitting of SFC and the energy-saving effects of each process are also obtained and discussed. The results show that combustion and heat-and-mass transfer processes have the largest SFC. Heat-and-mass transfer process and the vent process have the greatest avoidable SFCs. The closer the component to the final product, the larger its influence on the overall performance, and, thus, a small improvement to these components may lead to a large reduction in the overall fuel consumption. More effective energy-saving measures of coal-fired power plants should focus on the match of heat transfer at intermediate-and-low temperature level and the breakage of the isolation of heat transfer subsystems, especially enhancing the interaction between the air preheating process and feedwater preheating process