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Given a predicate $P: \{-1, 1\}^k \to \{-1, 1\}$, let $CSP(P)$ be the set of constraint satisfaction problems whose constraints are of the form $P$. We say that $P$ is approximable if given a nearly satisfiable instance of $CSP(P)$, there…

Computational Complexity · Computer Science 2020-04-28 Neng Huang , Aaron Potechin

The nonlinear model of the best-worst method frequently produces multiple optimal weight sets, which are conventionally determined through optimization software. While an analytical approach exists that provides both a closed-form…

Optimization and Control · Mathematics 2026-02-02 Harshit M. Ratandhara , Mohit Kumar

We investigate the problem of determining a set S of k indistinguishable integers in the range [1,n]. The algorithm is allowed to query an integer $q\in [1,n]$, and receive a response comparing this integer to an integer randomly chosen…

Data Structures and Algorithms · Computer Science 2013-02-06 Mark Braverman , Gal Oshri

We examine the evolution of the best choice algorithm and the probability of its success from a directed path to the linear order of the same cardinality through $k$th powers of a directed path, $1 \leq k < n$. The vertices of a $k$th power…

Combinatorics · Mathematics 2013-08-13 Andrzej Grzesik , Michał Morayne , Małgorzata Sulkowska

Several goal-oriented problems in the real-world can be naturally expressed as Stochastic Shortest Path Problems (SSPs). However, the computational complexity of solving SSPs makes finding solutions to even moderately sized problems…

Artificial Intelligence · Computer Science 2022-10-12 Rushang Karia , Rashmeet Kaur Nayyar , Siddharth Srivastava

PPSZ, for long time the fastest known algorithm for $k$-SAT, works by going through the variables of the input formula in random order; each variable is then set randomly to $0$ or $1$, unless the correct value can be inferred by an…

Data Structures and Algorithms · Computer Science 2024-08-07 Dominik Scheder

In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does…

Statistics Theory · Mathematics 2010-10-18 Andrey Novikov

There are two major models of value uncertainty in the optimal stopping literature: the secretary model, which assumes no prior knowledge, and the prophet inequality model, which assumes full information about value distributions. In…

Data Structures and Algorithms · Computer Science 2026-03-03 Tian Bai , Zhiyi Huang , Chui Shan Lee , Dongchen Li

A seminal result of H\r{a}stad [J. ACM, 48(4):798--859, 2001] shows that it is NP-hard to find an assignment that satisfies $\frac{1}{|G|}+\varepsilon$ fraction of the constraints of a given $k$-LIN instance over an abelian group, even if…

Computational Complexity · Computer Science 2020-09-08 Amey Bhangale , Subhash Khot

In many real world problems, we are faced with the problem of selecting the best among a finite number of alternatives, where the best alternative is determined based on context specific information. In this work, we study the contextual…

Optimization and Control · Mathematics 2022-01-20 Sait Cakmak , Siyang Gao , Enlu Zhou

In this work, we show the first worst-case to average-case reduction for the classical $k$-SUM problem. A $k$-SUM instance is a collection of $m$ integers, and the goal of the $k$-SUM problem is to find a subset of $k$ elements that sums to…

Computational Complexity · Computer Science 2020-11-12 Zvika Brakerski , Noah Stephens-Davidowitz , Vinod Vaikuntanathan

The $k$-Server Problem covers plenty of resource allocation scenarios, and several variations have been studied extensively for decades. We present a model generalizing the $k$-Server Problem by preferences of the requests, where the…

Data Structures and Algorithms · Computer Science 2022-10-21 Jannik Castenow , Björn Feldkord , Till Knollmann , Manuel Malatyali , Friedhelm Meyer auf der Heide

Uncertainty arises naturally inmany application domains due to, e.g., data entry errors and ambiguity in data cleaning. Prior work in incomplete and probabilistic databases has investigated the semantics and efficient evaluation of ranking…

Databases · Computer Science 2023-05-04 Su Feng , Boris Glavic , Oliver Kennedy

The last success problem is an optimal stopping problem that aims to maximize the probability of stopping on the last success in a sequence of independent $n$ Bernoulli trials. In the classical setting where complete information about the…

Probability · Mathematics 2024-07-24 Toru Yoshinaga , Yasushi Kawase

Let the sequence S_m of nonnegative integers be generated by the following conditions: Set the first term a_0 = 0, and for all k \geq 0, let a_k+1 be the least integer greater than a_k such that no element of {a_0,...,a_k+1} is the average…

Combinatorics · Mathematics 2011-07-12 Dennis Tseng

The objective of this paper is to show that the so-called unified approach to stopping problems with unknown cardinality introduced in Bruss (1984) proves to be efficient for solving other types of best-choice problems. We show that what we…

Probability · Mathematics 2016-10-03 Rémi Dendievel

Generalizing a problem posed by Cover, we propose an adversarial game in which a permutation is incrementally constructed in a setting of partial information. As in the secretary problem, this permutation is exposed in stages via the…

Probability · Mathematics 2018-09-13 Benjamin Diamond

We study generalizations of the "Prophet Inequality" and "Secretary Problem", where the algorithm is restricted to an arbitrary downward-closed set system. For {0,1}-values, we give O(log n)-competitive algorithms for both problems. This is…

Data Structures and Algorithms · Computer Science 2024-09-05 Aviad Rubinstein

The prophet secretary problem is a combination of the prophet inequality and the secretary problem, where elements are drawn from known independent distributions and arrive in uniformly random order. In this work, we design 1) a…

Data Structures and Algorithms · Computer Science 2024-11-05 Ziyun Chen , Zhiyi Huang , Dongchen Li , Zhihao Gavin Tang

In a prophet inequality problem, $n$ independent random variables are presented to a gambler one by one. The gambler decides when to stop the sequence and obtains the most recent value as reward. We evaluate a stopping rule by the…

Data Structures and Algorithms · Computer Science 2023-11-16 Andrés Cristi , Bruno Ziliotto