scholarly journals Approximating nash social welfare under rado valuations

2021 ◽  
Vol 19 (1) ◽  
pp. 45-51
Author(s):  
Jugal Garg ◽  
Edin Husić ◽  
László A. Végh
Keyword(s):  
Approximation Algorithm ◽  
Social Welfare ◽  
Geometric Mean ◽  
Constant Factor ◽  
Common Generalization ◽  
Welfare Problem ◽  
Allocation Of Indivisible Items ◽  
Rank Functions

The Nash social welfare problem asks for an allocation of indivisible items to agents in order to maximize the geometric mean of agents' valuations. We give an overview of the constant-factor approximation algorithm for the problem when agents have Rado valuations [Garg et al. 2021]. Rado valuations are a common generalization of the assignment (OXS) valuations and weighted matroid rank functions. Our approach also gives the first constant-factor approximation algorithm for the asymmetric Nash social welfare problem under the same valuations, provided that the maximum ratio between the weights is bounded by a constant.

scholarly journals Uniform Welfare Guarantees Under Identical Subadditive Valuations

2020 ◽  
Author(s):  
Siddharth Barman ◽  
Ranjani G. Sundaram
Keyword(s):  
Approximation Algorithm ◽  
Social Welfare ◽  
Constant Factor ◽  
Indivisible Goods ◽  
Generalized Mean ◽  
Single Allocation

We study the problem of allocating indivisible goods among agents that have an identical subadditive valuation over the goods. The extent of fair- ness and efficiency of allocations is measured by the generalized means of the values that the alloca- tions generate among the agents. Parameterized by an exponent term p, generalized-mean welfares en- compass multiple well-studied objectives, such as social welfare, Nash social welfare, and egalitarian welfare. We establish that, under identical subadditive valu- ations and in the demand oracle model, one can efficiently find a single allocation that approximates the optimal generalized-mean welfare—to within a factor of 40—uniformly for all p ∈ (−∞,1]. Hence, by way of a constant-factor approximation algorithm, we obtain novel results for maximizing Nash social welfare and egalitarian welfare for identical subadditive valuations.

scholarly journals Constant factor approximation algorithm for TSP satisfying a biased triangle inequality

2017 ◽  
Vol 657 ◽  
pp. 111-126 ◽  
Author(s):  
Usha Mohan ◽  
Sivaramakrishnan Ramani ◽  
Sounaka Mishra
Keyword(s):  
Approximation Algorithm ◽  
Triangle Inequality ◽  
Constant Factor

scholarly journals Randomized heuristic for the maximum clique problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Approximation Algorithm ◽  
Randomized Algorithm ◽  
Maximum Clique ◽  
Constant Factor ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Java Code ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all directly connected</p><p>to each other i.e. a complete sub-graph. A clique of the largest size is</p><p>called a maximum clique. Finding the maximum clique in a graph is an</p><p>NP-hard problem and it cannot be solved by an approximation algorithm</p><p>that returns a solution within a constant factor of the optimum. In this</p><p>work, we present a simple and very fast randomized algorithm for the</p><p>maximum clique problem. We also provide Java code of the algorithm</p><p>in our git repository. Results show that the algorithm is able to find</p><p>reasonably good solutions to some randomly chosen DIMACS benchmark</p><p>graphs. Rather than aiming for optimality, we aim to find good solutions</p><p>very fast.</p>

scholarly journals Randomized heuristic for the maximum clique problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Approximation Algorithm ◽  
Randomized Algorithm ◽  
Maximum Clique ◽  
Constant Factor ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Java Code ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all directly connected</p><p>to each other i.e. a complete sub-graph. A clique of the largest size is</p><p>called a maximum clique. Finding the maximum clique in a graph is an</p><p>NP-hard problem and it cannot be solved by an approximation algorithm</p><p>that returns a solution within a constant factor of the optimum. In this</p><p>work, we present a simple and very fast randomized algorithm for the</p><p>maximum clique problem. We also provide Java code of the algorithm</p><p>in our git repository. Results show that the algorithm is able to find</p><p>reasonably good solutions to some randomly chosen DIMACS benchmark</p><p>graphs. Rather than aiming for optimality, we aim to find good solutions</p><p>very fast.</p>

scholarly journals THE ROLE OF ENGLISH EDUCATION AS THE SOLUTION OF THE SOCIAL WELFARE PROBLEM IN INDONESIA

2016 ◽  
Vol 4 (2) ◽  
pp. 186
Author(s):  
Anisah Setyaningrum
Keyword(s):  
Social Welfare ◽  
English Education ◽  
The Other ◽  
Level Of Education ◽  
Welfare Level ◽  
International Language ◽  
The Social ◽  
Welfare Problem ◽  
Compulsory Subject

<p>The problem of social welfare becomes the theme which has been often to be discussed. This paper aims to describe the role of English Education as the solution of society’s welfare problem in Indonesia. English as an international language has become a compulsory subject in every level of education since last two decades. There are many advantages that can be gained by mastering English well, one of them is able to improve someone’s welfare level. One of the roles of English in increasing the Indonesian society’s welfare is English can be a potential provision in conducting entrepreneurship. In the other hand, it will increase their income. Besides, by having a good English mastery can facilitate them in gaining a better job.</p><p> </p>

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