Publications related to A note on the integrality gap of the configuration LP for restricted Santa Claus

Approximation Algorithms for Allocation and Network Design

In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...

EPFL2023

Discrete Optimal Transport with Independent Marginals is #P-Hard

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Bahar Taskesen

We study the computational complexity of the optimal transport problem that evaluates the Wasser- stein distance between the distributions of two K-dimensional discrete random vectors. The best known algorithms for this problem run in polynomial time in th ...

2022

Further Collapses in TFNP

Mika Tapani Göös, Gilbert Théodore Maystre, Alexandros Paul Hollender, Siddhartha Jain, Ran Tao

We show EOPL = PLS ∩ PPAD. Here the class EOPL consists of all total search problems that reduce to the End-of-Potential-Line problem, which was introduced in the works by Hubáček and Yogev (SICOMP 2020) and Fearnley et al. (JCSS 2020). In particular, our ...

Schloss Dagstuhl - Leibniz-Zentrum für Informatik2022

A (2+epsilon)-Approximation Algorithm for Preemptive Weighted Flow Time on a Single Machine

Lars Rohwedder

Weighted flow time is a fundamental and very well-studied objective function in scheduling. In this paper, we study the setting of a single machine with preemptions. The input consists of a set of jobs, characterized by their processing times, release time ...

ASSOC COMPUTING MACHINERY2021

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

,

b \in \Z^m

,

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

New Graph Algorithms via Polyhedral Techniques

Jakub Tarnawski

In this thesis we give new algorithms for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. S ...

EPFL2019

On approximation algorithms and polyhedral relaxations for knapsack problems, and clustered planarity testing

Igor Malinovic

Knapsack problems give a simple framework for decision making. A classical example is the min-knapsack problem (MinKnap): choose a subset of items with minimum total cost, whose total profit is above a given threshold. While this model successfully general ...

EPFL2019

Small Extended Formulation for Knapsack Cover Inequalities from Monotone Circuits

Ola Nils Anders Svensson, Abbas Bazzi, Sangxia Huang

Initially developed for the min-knapsack problem, the knapsack cover inequalities are used in the current best relaxations for numerous combinatorial optimization problems of covering type. In spite of their widespread use, these inequalities yield linear ...

UNIV CHICAGO, DEPT COMPUTER SCIENCE2018

Strengths and Limitations of Linear Programming Relaxations

Abbas Bazzi

Many of the currently best-known approximation algorithms for NP-hard optimization problems are based on Linear Programming (LP) and Semi-definite Programming (SDP) relaxations. Given its power, this class of algorithms seems to contain the most favourable ...

EPFL2017

Combinatorial Algorithm for Restricted Max-Min Fair Allocation

Ola Nils Anders Svensson, Christos Kalaitzis, Chidambaram Annamalai

We study the basic allocation problem of assigning resources to players to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, a certain ...

Association for Computing Machinery2017

A note on the integrality gap of the configuration LP for restricted Santa Claus

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Approximation Algorithms for Allocation and Network Design

Discrete Optimal Transport with Independent Marginals is #P-Hard

Further Collapses in TFNP

A (2+epsilon)-Approximation Algorithm for Preemptive Weighted Flow Time on a Single Machine

New Results in Integer and Lattice Programming

New Graph Algorithms via Polyhedral Techniques

On approximation algorithms and polyhedral relaxations for knapsack problems, and clustered planarity testing

Small Extended Formulation for Knapsack Cover Inequalities from Monotone Circuits

Strengths and Limitations of Linear Programming Relaxations

Combinatorial Algorithm for Restricted Max-Min Fair Allocation

Approximation Algorithms for Allocation and Network Design

Further Collapses in TFNP

Discrete Optimal Transport with Independent Marginals is #P-Hard

New Results in Integer and Lattice Programming

A (2+epsilon)-Approximation Algorithm for Preemptive Weighted Flow Time on a Single Machine

Strengths and Limitations of Linear Programming Relaxations

On approximation algorithms and polyhedral relaxations for knapsack problems, and clustered planarity testing

New Graph Algorithms via Polyhedral Techniques

Combinatorial Algorithm for Restricted Max-Min Fair Allocation

Small Extended Formulation for Knapsack Cover Inequalities from Monotone Circuits