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Related papers: Graphical Cake Cutting via Maximin Share

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We study truthful mechanisms for allocation problems in graphs, both for the minimization (i.e., scheduling) and maximization (i.e., auctions) setting. The minimization problem is a special case of the well-studied unrelated machines…

Computer Science and Game Theory · Computer Science 2021-06-08 George Christodoulou , Elias Koutsoupias , Annamaria Kovacs

Normalized-cut graph partitioning aims to divide the set of nodes in a graph into $k$ disjoint clusters to minimize the fraction of the total edges between any cluster and all other clusters. In this paper, we consider a fair variant of the…

Machine Learning · Computer Science 2023-10-10 Jia Li , Yanhao Wang , Arpit Merchant

The emerging theory of graph limits exhibits an analytic perspective on graphs, showing that many important concepts and tools in graph theory and its applications can be described more naturally (and sometimes proved more easily) in…

Combinatorics · Mathematics 2023-08-01 Omri Ben-Eliezer , Eldar Fischer , Amit Levi , Yuichi Yoshida

We consider the setting of repeated fair division between two players, denoted Alice and Bob, with private valuations over a cake. In each round, a new cake arrives, which is identical to the ones in previous rounds. Alice cuts the cake at…

Computer Science and Game Theory · Computer Science 2024-02-20 Simina Brânzei , MohammadTaghi Hajiaghayi , Reed Phillips , Suho Shin , Kun Wang

We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…

Computer Vision and Pattern Recognition · Computer Science 2016-01-12 Jörg Hendrik Kappes , Paul Swoboda , Bogdan Savchynskyy , Tamir Hazan , Christoph Schnörr

We consider the max-cut and max-$k$-cut problems under graph-based constraints. Our approach can handle any constraint specified using monadic second-order (MSO) logic on graphs of constant treewidth. We give a $\frac{1}{2}$-approximation…

Computational Complexity · Computer Science 2018-10-19 Martin Koutecký , Jon Lee , Viswanath Nagarajan , Xiangkun Shen

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…

Data Structures and Algorithms · Computer Science 2015-07-03 MohammadTaghi Hajiaghayi , Guy Kortsarz , Robert MacDavid , Manish Purohit , Kanthi Sarpatwar

The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…

Data Structures and Algorithms · Computer Science 2023-12-08 Franka Bause , Christian Permann , Nils M. Kriege

Motivated by the controller placement problems in software-defined networks and the fair division principles of classical "cake cutting", we investigate the following two-player zero-sum game. In our model, a defender places a limited…

Computational Complexity · Computer Science 2026-05-19 Grzegorz Gutowski , Konstanty Junosza-Szaniawski , Antonio Lauerbach , Alexander Wolff

We characterize methods of dividing a cake between two bidders in a way that is incentive-compatible and Pareto-efficient. In our cake cutting model, each bidder desires a subset of the cake (with a uniform value over this subset), and is…

Computer Science and Game Theory · Computer Science 2012-10-02 Avishay Maya , Noam Nisan

Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data.…

Statistics Theory · Mathematics 2019-09-06 Arash A. Amini , Bryon Aragam , Qing Zhou

We present a graphical approach to deriving inequality constraints for directed acyclic graph (DAG) models, where some variables are unobserved. In particular we show that the observed distribution of a discrete model is always restricted…

Statistics Theory · Mathematics 2012-09-14 Robin J. Evans

Given a non empty set $S$ of vertices of a graph, the partiality of a vertex with respect to $S$ is the difference between maximum and minimum of the distances of the vertex to the vertices of $S$. The vertices with minimum partiality…

Discrete Mathematics · Computer Science 2013-04-25 R. Ram Kumar , Kannan Balakrishnan , Prasanth G. Narasimha-Shenoi

We study separating systems of the edges of a graph where each member of the separating system is a path. We conjecture that every $n$-vertex graph admits a separating path system of size $O(n)$ and prove this in certain interesting special…

We study the problem of fair allocation of a set of indivisible items among agents with additive valuations, under cardinality constraints. In this setting, the items are partitioned into categories, each with its own limit on the number of…

Computer Science and Game Theory · Computer Science 2022-08-11 Halvard Hummel , Magnus Lie Hetland

A cut of a graph can be represented in many different ways. Here we propose to represent a cut through a ``relation tree'', which is a spanning tree with signed edges. We show that this picture helps to classify the main greedy heuristics…

Quantum Physics · Physics 2023-12-19 Jianan Wang , Chuixiong Wu , Fen Zuo

While there have been many results on lower bounds for Max Cut in unweighted graphs, there are only few results for lower bounds for Max Cut in weighted graphs. In this paper, we launch an extensive study of lower bounds for Max Cut in…

Combinatorics · Mathematics 2024-08-13 Gregory Gutin , Anders Yeo

For a given graph G and integers b,f >= 0, let S be a subset of vertices of G of size b+1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every…

Data Structures and Algorithms · Computer Science 2008-05-05 Fedor V. Fomin , Yngve Villanger

We study a fair division problem with indivisible items, namely the computation of maximin share allocations. Given a set of $n$ players, the maximin share of a single player is the best she can guarantee to herself, if she would partition…

Computer Science and Game Theory · Computer Science 2016-05-16 Georgios Amanatidis , Georgios Birmpas , Evangelos Markakis

In Fair AI literature, the practice of maliciously creating unfair models that nevertheless satisfy fairness constraints is known as "cherry-picking". A cherry-picking model is a model that makes mistakes on purpose, selecting bad…

Machine Learning · Computer Science 2024-12-20 Marco Favier , Toon Calders