Truthful Facility Assignment with Resource Augmentation: An Exact Analysis of Serial Dictatorship

We study the truthful facility assignment problem, where a set of agents with private most-preferred points on a metric space are assigned to facilities that lie on the metric space, under capacity constraints on the facilities. The goal is to produce such an assignment that minimizes the social cost, i.e., the total distance between the most-preferred points of the agents and their corresponding facilities in the assignment, under the constraint of truthfulness, which ensures that agents do not misreport their most-preferred points. We propose a resource augmentation framework, where a truthful mechanism is evaluated by its worst-case performance on an instance with enhanced facility capacities against the optimal mechanism on the same instance with the original capacities. We study a very well-known mechanism, Serial Dictatorship, and provide an exact analysis of its performance. Although Serial Dictatorship is a purely combinatorial mechanism, our analysis uses linear programming; a linear program expresses its greedy nature as well as the structure of the input, and finds the input instance that enforces the mechanism have its worst-case performance. Bounding the objective of the linear program using duality arguments allows us to compute tight bounds on the approximation ratio. Among other results, we prove that Serial Dictatorship has approximation ratio $g/(g-2)$ when the capacities are multiplied by any integer $g \geq 3$. Our results suggest that even a limited augmentation of the resources can have wondrous effects on the performance of the mechanism and in particular, the approximation ratio goes to 1 as the augmentation factor becomes large. We complement our results with bounds on the approximation ratio of Random Serial Dictatorship, the randomized version of Serial Dictatorship, when there is no resource augmentation

Depth-Independent Lower bounds on the Communication Complexity of Read-Once Boolean Formulas

We show lower bounds of $\Omega(\sqrt{n})$ and $\Omega(n^{1/4})$ on the randomized and quantum communication complexity, respectively, of all $n$-variable read-once Boolean formulas. Our results complement the recent lower bound of $\Omega(n/8^d)$ by Leonardos and Saks and $\Omega(n/2^{\Omega(d\log d)})$ by Jayram, Kopparty and Raghavendra for randomized communication complexity of read-once Boolean formulas with depth $d$. We obtain our result by "embedding" either the Disjointness problem or its complement in any given read-once Boolean formula.Comment: 5 page

Competitive Analysis for Two Variants of Online Metric Matching Problem

14th International Conference, COCOA 2020, Dallas, TX, USA, December 11–13, 2020

Competitive Analysis for Two Variants of Online Metric Matching Problem

In this paper, we study two variants of the online metric matching problem. The first problem is the online metric matching problem where all the servers are placed at one of two positions in the metric space. We show that a simple greedy algorithm achieves the competitive ratio of 3 and give a matching lower bound. The second problem is the online facility assignment problem on a line, where servers have capacities, servers and requests are placed on 1-dimensional line, and the distances between any two consecutive servers are the same. We show lower bounds $1+ \sqrt{6}$ $(> 3.44948)$, $\frac{4+\sqrt{73}}{3}$ $(>4.18133)$ and $\frac{13}{3}$ $(>4.33333)$ on the competitive ratio when the numbers of servers are 3, 4 and 5, respectively.Comment: 12 pages. Update from the 1st version: The first author was added and Theorems 3, 4 and 5 were improve

Improved Quantum Communication Complexity Bounds for Disjointness and Equality

We prove new bounds on the quantum communication complexity of the disjointness and equality problems. For the case of exact and non-deterministic protocols we show that these complexities are all equal to n+1, the previous best lower bound being n/2. We show this by improving a general bound for non-deterministic protocols of de Wolf. We also give an O(sqrt{n}c^{log^* n})-qubit bounded-error protocol for disjointness, modifying and improving the earlier O(sqrt{n}log n) protocol of Buhrman, Cleve, and Wigderson, and prove an Omega(sqrt{n}) lower bound for a large class of protocols that includes the BCW-protocol as well as our new protocol.Comment: 11 pages LaTe

The chromatic discrepancy of graphs

For a proper vertex coloring cc of a graph GG, let φc(G)φc(G) denote the maximum, over all induced subgraphs HH of GG, the difference between the chromatic number χ(H)χ(H) and the number of colors used by cc to color HH. We define the chromatic discrepancy of a graph GG, denoted by φ(G)φ(G), to be the minimum φc(G)φc(G), over all proper colorings cc of GG. If HH is restricted to only connected induced subgraphs, we denote the corresponding parameter by View the MathML sourceφˆ(G). These parameters are aimed at studying graph colorings that use as few colors as possible in a graph and all its induced subgraphs. We study the parameters φ(G)φ(G) and View the MathML sourceφˆ(G) and obtain bounds on them. We obtain general bounds, as well as bounds for certain special classes of graphs including random graphs. We provide structural characterizations of graphs with φ(G)=0φ(G)=0 and graphs with View the MathML sourceφˆ(G)=0. We also show that computing these parameters is NP-hard

Selênio como suplemento para bovinos intoxicados cronicamente por Pteridium sp. no Espirito Santo. 2017.

Pteridiumsp.(samambaia) é uma planta responsável por diversos quadros de intoxicação em animais e seres humanos. Em bovinos, um dos quadros comuns na região sul do Espírito Santo é a hematúria enzoótica bovina (HEB) que não possui tratamento. Assim, o objetivo do presente trabalho foi determinar os efeitos do selênio associado a vitamina E como suplemento em animais intoxicados cronicamente pelo Pteridium sp. Foram selecionados 21 animais intoxicados cronicamente pela planta e com HEB. Os animais foram examinados clinicamente e foi realizada a coleta da urina para a confirmação da hematúria. O delineamento experimental foi feito em quatro grupos divididos ao acaso (controle soro fisiológico; tratamento 1 0,05 mg/Kg do suplemento;tratamento20,10mg/Kgdosuplemento;tratamento30,20mg/Kgdo suplemento). Foi feita a suplementação parenteral, via intramuscular, uma vez por semana, durante 13 semanas. Quinzenalmente os animais foram avaliados clinicamente e foram coletadas amostras de sangue para dosagem do selêniosérico. A análise de selênio foi feita nos momentos inicial, antes da suplementação com selênio (M0), após quatro semanas de tratamento (M4), após oito semanas (M8) e após 12 semanas (M12), pelo método de espectrofotometria de absorção atômica. Utilizou-seaanálisedevariância(ANOVA)seguidadotestedeTukeya5%.Verificou-se que houve maior ganho de peso dos animais tratados com selênio em relação ao grupocontrolee,também,entreosgrupos.Aintensidadedahematúriareduziuapartir da sexta semana e houve diferença significativa entre os grupos tratados e o grupo controle, assim como entre os grupos. Houve diferença significativa da concentração sérica de selênio entre os tratamentos. Assim, conclui-se que o selênio associado a vitaminaEcomosuplementoparabovinosintoxicadoscronicamenteporPteridiumsp. no Espirito Santo com quadro de HEB teve efeito dose dependente sobre a melhora doquadroclínicocausandoreduçãodaintensidadedehematúriaeaumentodoganho de pes