Deterministic Rounding of Dynamic Fractional Matchings

We present a framework for deterministically rounding a dynamic fractional matching. Applying our framework in a black-box manner on top of existing fractional matching algorithms, we derive the following new results: (1) The first deterministic algorithm for maintaining a (2-?)-approximate maximum matching in a fully dynamic bipartite graph, in arbitrarily small polynomial update time. (2) The first deterministic algorithm for maintaining a (1+?)-approximate maximum matching in a decremental bipartite graph, in polylogarithmic update time. (3) The first deterministic algorithm for maintaining a (2+?)-approximate maximum matching in a fully dynamic general graph, in small polylogarithmic (specifically, O(log? n)) update time. These results are respectively obtained by applying our framework on top of the fractional matching algorithms of Bhattacharya et al. [STOC\u2716], Bernstein et al. [FOCS\u2720], and Bhattacharya and Kulkarni [SODA\u2719]. Previously, there were two known general-purpose rounding schemes for dynamic fractional matchings. Both these schemes, by Arar et al. [ICALP\u2718] and Wajc [STOC\u2720], were randomized. Our rounding scheme works by maintaining a good matching-sparsifier with bounded arboricity, and then applying the algorithm of Peleg and Solomon [SODA\u2716] to maintain a near-optimal matching in this low arboricity graph. To the best of our knowledge, this is the first dynamic matching algorithm that works on general graphs by using an algorithm for low-arboricity graphs as a black-box subroutine. This feature of our rounding scheme might be of independent interest

Incremental (1−ϵ)(1-\epsilon)-approximate dynamic matching in O(poly(1/ϵ))O(poly(1/\epsilon)) update time

In the dynamic approximate maximum bipartite matching problem we are given bipartite graph $G$ undergoing updates and our goal is to maintain a matching of $G$ which is large compared the maximum matching size $\mu(G)$. We define a dynamic matching algorithm to be $\alpha$ (respectively $(\alpha, \beta)$)-approximate if it maintains matching $M$ such that at all times $|M | \geq \mu(G) \cdot \alpha$ (respectively $|M| \geq \mu(G) \cdot \alpha - \beta$). We present the first deterministic $(1-\epsilon )$-approximate dynamic matching algorithm with $O(poly(\epsilon ^{-1}))$ amortized update time for graphs undergoing edge insertions. Previous solutions either required super-constant [Gupta FSTTCS'14, Bhattacharya-Kiss-Saranurak SODA'23] or exponential in $1/\epsilon$ [Grandoni-Leonardi-Sankowski-Schwiegelshohn-Solomon SODA'19] update time. Our implementation is arguably simpler than the mentioned algorithms and its description is self contained. Moreover, we show that if we allow for additive $(1, \epsilon \cdot n)$-approximation our algorithm seamlessly extends to also handle vertex deletions, on top of edge insertions. This makes our algorithm one of the few small update time algorithms for $(1-\epsilon )$-approximate dynamic matching allowing for updates both increasing and decreasing the maximum matching size of $G$ in a fully dynamic manner

Incremental (1-?)-Approximate Dynamic Matching in O(poly(1/?)) Update Time

In the dynamic approximate maximum bipartite matching problem we are given bipartite graph G undergoing updates and our goal is to maintain a matching of G which is large compared the maximum matching size ?(G). We define a dynamic matching algorithm to be ? (respectively (?, ?))-approximate if it maintains matching M such that at all times |M | ? ?(G) ? ? (respectively |M| ? ?(G) ? ? - ?). We present the first deterministic (1-?)-approximate dynamic matching algorithm with O(poly(?^{-1})) amortized update time for graphs undergoing edge insertions. Previous solutions either required super-constant [Gupta FSTTCS\u2714, Bhattacharya-Kiss-Saranurak SODA\u2723] or exponential in 1/? [Grandoni-Leonardi-Sankowski-Schwiegelshohn-Solomon SODA\u2719] update time. Our implementation is arguably simpler than the mentioned algorithms and its description is self contained. Moreover, we show that if we allow for additive (1, ??n)-approximation our algorithm seamlessly extends to also handle vertex deletions, on top of edge insertions. This makes our algorithm one of the few small update time algorithms for (1-?)-approximate dynamic matching allowing for updates both increasing and decreasing the maximum matching size of G in a fully dynamic manner. Our algorithm relies on the weighted variant of the celebrated Edge-Degree-Constrained-Subgraph (EDCS) datastructure introduced by [Bernstein-Stein ICALP\u2715]. As far as we are aware we introduce the first application of the weighted-EDCS for arbitrarily dense graphs. We also present a significantly simplified proof for the approximation ratio of weighed-EDCS as a matching sparsifier compared to [Bernstein-Stein], as well as simple descriptions of a fractional matching and fractional vertex cover defined on top of the EDCS. Considering the wide range of applications EDCS has found in settings such as streaming, sub-linear, stochastic and more we hope our techniques will be of independent research interest outside of the dynamic setting

A model for a knowledge-based system's life cycle

The American Institute of Aeronautics and Astronautics has initiated a Committee on Standards for Artificial Intelligence. Presented here are the initial efforts of one of the working groups of that committee. The purpose here is to present a candidate model for the development life cycle of Knowledge Based Systems (KBS). The intent is for the model to be used by the Aerospace Community and eventually be evolved into a standard. The model is rooted in the evolutionary model, borrows from the spiral model, and is embedded in the standard Waterfall model for software development. Its intent is to satisfy the development of both stand-alone and embedded KBSs. The phases of the life cycle are detailed as are and the review points that constitute the key milestones throughout the development process. The applicability and strengths of the model are discussed along with areas needing further development and refinement by the aerospace community

Cost of compliance with the aquis communautaire in the Hungarian dairy sector

The implementation and enforcement of the acquis communautaire is a precondition for joining the European Union (EU). However, there is only little information on the compliance costs in the acceding countries. In this paper, the investment needs and annual costs of compliance with the part of the acquis communautaire relevant for the dairy sector is assessed at different stages of the agri-food chain in Hungary. The assessment is mainly based on a classification of farms and processors according to their level of compliance with EU standards concerning milk hygiene in 2000/01 and calculations of necessary investments in buildings, milking and cooling facilities and delivery trucks. The raw milk quality in Hungary has steadily improved since the early 1990's. In 1999, 78 % of the milk delivered to processors was in compliance with EU standards. Based on the farm structure in the reference period, the further necessary modernisation requires investments of 82 million euro causing annual compliance costs of 9 million euro or 0.1 up to 4.3 cent per litre milk. This is equivalent to 0.6 % up to 17.9 % of the average farm gate price for milk in 2000. For modernising the milk collection centres, 25 million euro are needed, and for the delivery trucks between 12 million euro and 17 million euro. Depending on the size of the milk processor and the current level of compliance, the annual compliance costs are estimated to be low, ranging from negligible 0.02 cent per litre up to 0.7 cent per litre. Based on these findings there is only limited need for the government to support the further modernisation of milk processors. State support is more relevant at the farm level. Since 68 % of the total investment needs estimated at farm level are accounted for by farms with less than 5 cows, agricultural policy should support these farmers either to considerably increase their herd size or to cease production. -- G E R M A N V E R S I O N: Die Implementierung und Durchsetzung des acquis communautaire ist eine Voraussetzung für den Beitritt zur Europäischen Union (EU). Über die hiermit in den Beitrittsländern ver-bundenen Kosten liegen bisher kaum Informationen vor. In diesem Beitrag wird der Teil des acquis communautaire betrachtet, der für den Milchsektor in Ungarn von Bedeutung ist. Für verschiedene Stufen der Milcherzeugung und verarbeitung wird untersucht, welcher Investi-tionsbedarf zur Einhaltung der relevanten Vorschriften besteht und wie hoch die hieraus resultierenden kalkulatorischen und pagatorischen jährlichen Kosten sind. Die Abschätzung basiert im Wesentlichen auf einer Einteilung der Milcherzeugungs- und verarbeitungs-unternehmen nach dem Stand der Einhaltung der EU-Milchhygienestandards im Jahr 2000/01 und Kalkulationen der notwendigen Investitionen in Gebäude, Melk- und Kühltechnik sowie in Milchtransportfahrzeuge. Die Rohmilchqualität hat sich in Ungarn seit Anfang der 90er Jahre stetig verbessert. 1999 erfüllten bereits 78 % der an Molkereien gelieferten Milch die EU-Standards. Basierend auf der landwirtschaftlichen Betriebsstruktur in der Referenzperiode 2000/01 liegt der weitere Bedarf an Modernisierungsinvestitionen in einer Größenordnung von 82 Millionen Euro. Hieraus folgen jährliche Kosten in Höhe von 9 Millionen Euro oder 0,1 bis 4,3 Cent pro Liter Milch. Dies entspricht 0,6 % bis 17,9 % des 2000 durchschnittlich erzielten Erzeuger-preises für Milch. Zur Modernisierung der Milchsammelstellen werden etwa 25 Millionen Euro benötigt und für Milchtransportfahrzeuge zwischen 12 Millionen Euro und 17 Millionen Euro. In Abhängigkeit von der Größe der Molkereien und dem Grad der Einhaltung der EU-Standards in der Ausgangssituation ergeben sich jährliche Modernisierungskosten in einer geringen Größenordnung: Sie reichen von vernachlässigbaren 0,02 Cent pro Liter bis zu 0,7 Cent pro Liter. Die Ergebnisse zeigen, dass nur eine begrenzte Notwendigkeit für staatliche Hilfen zur Modernisierung des Milchverarbeitungssektors besteht. Auf der Erzeugerebene sind Förder-maßnahmen dagegen wichtiger. Weil 68 % des geschätzten gesamten Investitionsbedarfs auf Betriebe mit weniger als 5 Kühen entfällt, sollte die Agrarpolitik die Leiter dieser Betriebe dabei unterstützen, entweder ihre Produktion spürbar auszudehnen oder ganz einzustellen.Hungary,acquis communautaire,milk hygiene,dairy sector,modernisation,Ungarn,acquis communautaire,Milchhygiene,Milchsektor,Modernisierung

Assessing the Economic and Social Impact of Tax and Transfer System Reforms: A General Equilibrium Microsimulation Approach JRC Working Papers in Economics and Finance, 2017/9

We present a general-equilibrium behavioural microsimulation model designed to assess long-run macroeconomic, fiscal and social consequences of reforms to the tax and transfer system. The behaviour of labour supply is assessed along both the extensive and intensive margins, by merging the discrete choice and the elasticity of taxable income approaches. General-equilibrium feedback effects are simulated by embedding microsimulation in a parsimonious macro model of a small open economy. We estimate and calibrate the model to Hungary, and then perform three sets of simulations. The first one explores the impact of personal income tax reductions that are identical in cost but different in structure. The second one compares three different tax shift scenarios, while the third one evaluates actual policy measures between 2008 and 2013. The results suggest that while a cut in the marginal tax rate of high-income individuals may boost output, it does not have a significant employment effect. On the other hand, programs like the Employee Tax Credit do have a significant employment effect. We find that the policy measures introduced since 2008 substantially increase income inequality in the long run; the contribution of the changes after 2010 are about four times that of the changes before 2010. Our results highlight that taking account of household heterogeneity is crucial in the analysis of the macroeconomic effects of tax and transfer reforms.JRC.B.1-Finance and Econom

Sublinear Algorithms for (1.5+ϵ)(1.5+\epsilon)-Approximate Matching

We study sublinear time algorithms for estimating the size of maximum matching. After a long line of research, the problem was finally settled by Behnezhad [FOCS'22], in the regime where one is willing to pay an approximation factor of $2$. Very recently, Behnezhad et al.[SODA'23] improved the approximation factor to $(2-\frac{1}{2^{O(1/\gamma)}})$ using $n^{1+\gamma}$ time. This improvement over the factor $2$ is, however, minuscule and they asked if even $1.99$-approximation is possible in $n^{2-\Omega(1)}$ time. We give a strong affirmative answer to this open problem by showing $(1.5+\epsilon)$-approximation algorithms that run in $n^{2-\Theta(\epsilon^{2})}$ time. Our approach is conceptually simple and diverges from all previous sublinear-time matching algorithms: we show a sublinear time algorithm for computing a variant of the edge-degree constrained subgraph (EDCS), a concept that has previously been exploited in dynamic [Bernstein Stein ICALP'15, SODA'16], distributed [Assadi et al. SODA'19] and streaming [Bernstein ICALP'20] settings, but never before in the sublinear setting. Independent work: Behnezhad, Roghani and Rubinstein [BRR'23] independently showed sublinear algorithms similar to our Theorem 1.2 in both adjacency list and matrix models. Furthermore, in [BRR'23], they show additional results on strictly better-than-1.5 approximate matching algorithms in both upper and lower bound sides

Dynamic (1+ϵ)(1+\epsilon)-Approximate Matching Size in Truly Sublinear Update Time

We show a fully dynamic algorithm for maintaining $(1+\epsilon)$-approximate \emph{size} of maximum matching of the graph with $n$ vertices and $m$ edges using $m^{0.5-\Omega_{\epsilon}(1)}$ update time. This is the first polynomial improvement over the long-standing $O(n)$ update time, which can be trivially obtained by periodic recomputation. Thus, we resolve the value version of a major open question of the dynamic graph algorithms literature (see, e.g., [Gupta and Peng FOCS'13], [Bernstein and Stein SODA'16],[Behnezhad and Khanna SODA'22]). Our key technical component is the first sublinear algorithm for $(1,\epsilon n)$-approximate maximum matching with sublinear running time on dense graphs. All previous algorithms suffered a multiplicative approximation factor of at least $1.499$ or assumed that the graph has a very small maximum degree