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On Polynomial Algorithms for Normalizing Formulas

Viktor Kuncak, Simon Guilloud, Mario Bucev

We propose a new approach for normalization and simplification of logical formulas. Our approach is based on algorithms for lattice-like structures. Specifically, we present two efficient algorithms for computing a normal form and deciding the word problem ...

2022

Approximate CVPp in time 2(0.802n)

Friedrich Eisenbrand, Moritz Andreas Venzin

We show that a constant factor approximation of the shortest and closest lattice vector problem in any l(p)-norm can be computed in time 2((0.802 + epsilon)n). This matches the currently fastest constant factor approximation algorithm for the shortest vect ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Equivalence Checking for Orthocomplemented Bisemilattices in Log-Linear Time

Viktor Kuncak, Simon Guilloud

We present a quasilinear time algorithm to decide the word problem on a natural algebraic structures we call orthocomplemented bisemilattices, a subtheory of boolean algebra. We use as a base a variation of Hopcroft, Ullman and Aho algorithm for tree isomo ...

Springer2022

Sketches, metrics and fast algorithms

Navid Nouri

As it has become easier and cheaper to collect big datasets in the last few decades, designing efficient and low-cost algorithms for these datasets has attracted unprecedented attention. However, in most applications, even storing datasets as acquired has ...

EPFL2022

Beyond Time-Average Convergence: Near-Optimal Uncoupled Online Learning via Clairvoyant Multiplicative Weights Update

Efstratios Panteleimon Skoulakis

In this paper we provide a novel and simple algorithm, Clairvoyant Multiplicative Weights Updates (CMWU), for convergence to \textit{Coarse Correlated Equilibria} (CCE) in general games. CMWU effectively corresponds to the standard MWU algorithm but where ...

2022

Safety Verification for Urban Air Mobility Scheduling

Nils Gustav Nilsson

In Urban Air Mobility (UAM) networks, takeoff and landing sites, called vertiports, are likely to experience intermittent closures due to, e.g., adverse weather. For safety, it will be required that all in-transit Urban Air Vehicles (UAVs) in a UAM network ...

ELSEVIER2022

Faster Monotone Min-Plus Product, Range Mode, and Single Source Replacement Paths

Adam Teodor Polak

One of the most basic graph problems, All-Pairs Shortest Paths (APSP) is known to be solvable in n^{3-o(1)} time, and it is widely open whether it has an O(n^{3-ε}) time algorithm for ε > 0. To better understand APSP, one often strives to obtain subcubic t ...

Schloss Dagstuhl -- Leibniz-Zentrum für Informatik2021

How to Match in Modern Computational Settings

Buddhima Ruwanmini Gamlath Gamlath Ralalage

This thesis focuses on the maximum matching problem in modern computational settings where the algorithms have to make decisions with partial information.First, we consider two stochastic models called query-commit and price-of-information where the algori ...

EPFL2021

Computation Of A 30750-Bit Binary Field Discrete Logarithm

Arjen Lenstra, Robert Granger, Thorsten Kleinjung, Benjamin Pierre Charles Wesolowski

This paper reports on the computation of a discrete logarithm in the finite field F-230750, breaking by a large margin the previous record, which was set in January 2014 by a computation in F-29234. The present computation made essential use of the elimina ...

AMER MATHEMATICAL SOC2021

Knapsack and Subset Sum with Small Items

Adam Teodor Polak, Lars Rohwedder

Knapsack and Subset Sum are fundamental NP-hard problems in combinatorial optimization. Recently there has been a growing interest in understanding the best possible pseudopolynomial running times for these problems with respect to various parameters. In t ...

Schloss Dagstuhl -- Leibniz-Zentrum für Informatik2021