?
A polynomial-time algorithm for computing a Pareto optimal and almost proportional allocation
We consider fair allocation of indivisible items under additive utilities. When the utilities can be negative, the existence and complexity of an allocation that satisfies Pareto optimality and proportionality up to one item (PROP1) is an open problem. We show that there exists a strongly polynomial-time algorithm that always computes an allocation satisfying Pareto optimality and proportionality up to one item even if the utilities are mixed and the agents have asymmetric weights. We point out that the result does not hold if either of Pareto optimality or PROP1 is replaced with slightly stronger concepts.
Language:
English
Keywords: polynomial algorithmfair division of goods and badsPareto frontiertrading cyclesindivisible itemsProp1
Publication based on the results of:
Михайлов И. А., М.: ФГБУ "Издательство "Наука", 2023.
Предложены основные направления совершенствования планирования, организации и оплаты медицинской помощи, лекарственного обеспечения, информатизации и оценки технологий здравоохранения. Рекомендованы такие мероприятия, как конкретизация программы государственных гарантий бесплатного оказания гражданам медицинской помощи, создание системы общедоступного лекарственного обеспечения, использование клинико-статистических групп для оплаты медицинской помощи при ряде хронических неинфекционных заболеваний в амбулаторных условиях, формирование механизма привлечения соплатежей при ...
Added: July 16, 2026
Михайлов И. А., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 1 Article 8
Whole-slide histology images (WSIs) can exceed 100 k × 100 k pixels, making direct pixel-level segmentation infeasible and requiring patch-level classification as a practical alternative for downstream WSI segmentation. However, most approaches either treat patches independently, ignoring spatial and biological context, or rely on deep graph models prone to oversmoothing and loss of local tissue ...
Added: July 16, 2026
Emelyanova O., Восток. Афро-азиатские общества: история и современность 2024 No. 1 P. 153–164
Food security in Japan has been under observation of analytics in both Japan and abroad as it is one of the key national security issues. Leading academic researchers of this issue in Japan include Suzuki N., Takeya T.,Yamamoto R. and Oguchi H. However, the main focus of their analysis is the social aspect. The English ...
Added: July 16, 2026
Kuninets A., Malygina E., Leevik A. G. et al., Journal of Computer Virology and Hacking Techniques 2026 No. 22 Article 62
In this work, we investigate the application of Barnes–Wall lattices in post-quantum cryptographic schemes. We survey and analyze several constructions of Barnes–Wall lattices, including subgroup chains, the generalized k-ing construction, and connections with Reed-Muller codes, highlighting their equivalence over both Z[i] and Z. Building on these structural insights, we introduce a new algorithm for efficient ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Aleshin D., Бирюков Е. С., Булатов А. С. et al., Аспект Пресс, 2025.
Учебное пособие подготовлено коллективом российских экономистов-международников, преимущественно из МГИМО. Оно посвящено анализу особенностей незападных экономических систем, а также участия данных стран в международных экономических отношениях.
Структурно учебное пособие состоит из трех разделов и 23 глав. Первый раздел посвящен различным аспектам методологии анализа незападных экономических систем. Приводятся как современные западные концепции классификации экономических систем, так и критические, а также незападные подходы к развитию (в том числе периферийная ...
Added: July 15, 2026
Degterev D. A., Степанова В. С., Международное право и международные организации 2025 № 3 С. 93–109
The issues of monetary cooperation between France and the member states of the West African Monetary Union (WAMU) have received wide coverage in academic literature. However, the phenomenon of the CFA franc as the "last colonial currency" of Africa is considered mainly in a journalistic vein, in a political and historical context, less often – ...
Added: July 15, 2026
Degterev D. A., Кирикова Т. Н., Россия и мир: научный диалог 2025 № 4 С. 37–57
This study focuses on the African policy of the Trump administration during his second term. The authors analyze why the formal framework for strategic planning in Africa proved too restrictive for the new US administration. Particular attention is paid to the consistent decline in international aid as a part of US African strategy. During Trump’s ...
Added: July 15, 2026
Cham: Springer, 2026.
In this ambitious two-volume open access collection of essays, a diverse group of scholars worldwide reflects on the past, present and future of the (comparative) regionalism research program. Volume I provides building blocks for regionalism studies in the coming years by indicating what a pluralistic theoretical and methodological toolbox to study regions could look like, ...
Added: July 15, 2026
Karpova N. S., Союзное государство 2026 Т. 232 № 6, июнь С. 87–89
The article examines the peculiarities of the formation of Belarusian enterprises, the factors of their competitiveness, high export potential, and the culture of marketing work. The author raises the question of ways to strengthen integration processes within the Union State by understanding the competitive advantages of its participants, creating conditions for the growth of mutual ...
Added: July 14, 2026
Economies 2026 Vol. 14 No. 07 P. 277
The increasingly rapid process of de-dollarization in the context of growing geopolitical fragmentation has significantly altered the monetary dynamics of the global economy, thereby posing important questions about economic resilience and sustainable development in the emerging world. This research investigates de-dollarization-related macro-financial conditions and their association with economic resilience in the BRICS+ countries during the ...
Added: July 14, 2026
Silakov D., Системный администратор 2026 № 5 С. 46–51
В предыдущей статье про Open Source в КНР [1] мы рассказали про Alibaba – крупную корпорацию, занимающую тридцатое место в рейтинге самых значимых мировых брэндов за 2025 год [2]. Место почетное, но не первое среди китайских компаний – на тринадцатом месте расположилась Tencent, разработчик WeChat и ряда других продуктов, широко используемых нашими восточными соседями. Tencent ...
Added: July 14, 2026
Yusupova G. F., Вопросы экономики 2026 № 7 С. 70–91
The rules for collecting, processing and using personal information affect the
distribution of surpluses both between firms in markets and between firms and
consumers. Regulating the turnover of personal data is fundamental for sellers
in the digital economy, including digital platforms. To prevent the risks of pri
vacy violations and manipulation of consumer choice, the legislator restricts the
collection and ...
Added: July 13, 2026
Абрамова И. О., Аду Я. Н., Анише Т. Э. et al., Институт Африки РАН, 2025.
Данная монография посвящена анализу концепции суверенитета африканских государств как в теоретическом, так и практическом ключе. Рассматриваются экономический, ментальный, языковой и культурный, информационный и образовательный аспекты африканского суверенитета. Исследуется роль региональных интеграционных группировок, а также внешних акторов в контексте суверенизации Африки. Особое внимание уделяется роли РФ в укре- плении суверенитета стран континента.
Монография формирует целостное представление по ...
Added: July 13, 2026
IEEE, 2026.
Added: July 13, 2026
Switzerland: Springer, 2026.
This volume contains the refereed proceedings of the 25th International Conference on Mathematical Optimization Theory and Operations Research (MOTOR 2026) 1 held during July 6–11 in a picturesque place near Lake Baikal, Irkutsk, Russia. The MOTOR conference is a direct successor and scientific inheritor of several prominent events on mathematical programming, combinatorial and stochastic optimization, ...
Added: July 12, 2026
Шиманогов И. Н., Vyalyi M., Дискретный анализ и исследование операций 2025 Т. 32 № 4(166) С. 213–230
A well-studied class of algorithmic problems is that of regular realizability: checking the non-emptiness of the intersection of a regular language with a given language. This problem has a natural algebraic interpretation: verifying whether an element of a Boolean algebra belongs to the kernel of a certain homomorphism. This motivates the consideration of an analogous ...
Added: July 12, 2026
Grebnev L., Вопросы философии 2026 № 7 С. 5–15
In the coming millennium, the transformation of our world has become a matter
of global concern. The first attempts to move in this direction were unsuccessful.
The globalization of economic activity is being replaced by the formation of relatively
autonomous macroregions. But it would be a mistake to assume on this
basis that joint dominion over the entire planet ...
Added: July 11, 2026
Родичев А. И., Zinyakov Y., Вестник Московского университета. Серия 6: Экономика 2026 Т. 61 № 2 С. 340–357
This paper analyzes discrepancies between direct and mirror data in Russia's foreign trade statistics over the period of 2003-2024. Special attention is given to assessing the impact of sanction policies on the level of statistical discrepancies, which reflect trade costs, manipulations in customs and tax reporting, as well as structural changes in logistics and the ...
Added: July 10, 2026
Kuzminov Y., Kruchinskaia E., Вопросы экономики 2026 № 7 С. 5–27
The year 2026 marks the 250th anniversary of Adam Smith’s “An inquiry into the nature and causes of the wealth of nations”, the work that had laid the foundations of economic science. The three factors of production Smith implicitly introduced — labor, land, and capital — no longer operate in their pure form: the digital ...
Added: July 9, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Sizova A., Барнаул: Алтайский государственный педагогический университет, 2026.
В сборник включены научные статьи, посвященные различным аспектам социально-экономической и культурной истории Сибири в контексте внутренней и внешней политики России. Сборник посвящен 70-летию со дня рождения известного ученого, педагога, просветителя и общественного деятеля, доктора исторических наук, профессора Александра Владимировича Старцева (1956–2019).
Сборник предназначен для специалистов в области отечественного исторического сибиреведения, а также всех, кто интересуется историей ...
Added: July 8, 2026
Surkov A., Ignatenko V., Koltcov Sergei, Computers, Materials and Continua 2026
Large language models have recently demonstrated promising capabilities in mathematical reasoning; however, their performance on tasks requiring strict symbolic manipulation, such as solving differential equations, remains limited, especially for compact models. In this work, we investigate whether activation steering combined with reinforcement learning can improve the quality of solutions generated by pretrained language models without ...
Added: July 8, 2026