Related papers: A Variation of Levin Search for All Well-Defined P…
This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…
In this paper, we study the following problem of reconstructing a simple polygon: Given a cyclically ordered vertex sequence of an unknown simple polygon P of n vertices and, for each vertex v of P, the sequence of angles defined by all the…
Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…
We propose an anytime online algorithm for the problem of learning a sequence of adversarial convex cost functions while approximately satisfying another sequence of adversarial online convex constraints. A sequential algorithm is called…
We consider the problem of minimizing the total processing time of tardy jobs on a single machine. This is a classical scheduling problem, first considered by [Lawler and Moore 1969], that also generalizes the Subset Sum problem. Recently,…
We consider a problem first proposed by Mahler and Popken in 1953 and later developed by Coppersmith, Erd\H{o}s, Guy, Isbell, Selfridge, and others. Let $f(n)$ be the complexity of $n \in \mathbb{Z^{+}}$, where $f(n)$ is defined as the…
We present a novel algorithm that solves the turbo code LP decoding problem in a fininte number of steps by Euclidean distance minimizations, which in turn rely on repeated shortest path computations in the trellis graph representing the…
Given a set $\Pi$ of permutation patterns of length at most $k$, we present an algorithm for building $S_{\le n}(\Pi)$, the set of permutations of length at most $n$ avoiding the patterns in $\Pi$, in time $O(|S_{\le n - 1}(\Pi)| \cdot k +…
Levin Tree Search (LTS) (Orseau et al., 2018) is a search algorithm for deterministic environments that uses a user-specified policy to guide the search. It comes with a formal guarantee on the number of search steps (node visits) for…
In this work we revisit the elementary scheduling problem $1||\sum p_j U_j$. The goal is to select, among $n$ jobs with processing times and due dates, a subset of jobs with maximum total processing time that can be scheduled in sequence…
We consider integer programming problems $\max \{ c^T x : \mathcal{A} x = b, l \leq x \leq u, x \in \mathbb{Z}^{nt}\}$ where $\mathcal{A}$ has a (recursive) block-structure generalizing "$n$-fold integer programs" which recently received…
The theory of $n$-fold integer programming has been recently emerging as an important tool in parameterized complexity. The input to an $n$-fold integer program (IP) consists of parameter $A$, dimension $n$, and numerical data of binary…
Grover search is one of the most important quantum algorithms. In this paper, we consider a kind of search that the conditions of satisfaction $T$ can be rewritten as $T=T_1\bigcap T_2$. Then we present a new Grover search with smaller…
Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are…
We study variable time search, a form of quantum search where queries to different items take different time. Our first result is a new quantum algorithm that performs variable time search with complexity $O(\sqrt{T}\log n)$ where…
One specific subset of quantum algorithms is Grovers Ordered Search Problem (OSP), the quantum counterpart of the classical binary search algorithm, which utilizes oracle functions to produce a specified value within an ordered database.…
In the last twenty-five years (1990-2014), algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 200 billion factor speedup in solving Mixed Integer Optimization (MIO) problems. We…
In this article we dwell into the class of so called ill posed Linear Inverse Problems (LIP) in machine learning, which has become almost a classic in recent times. The fundamental task in an LIP is to recover the entire signal / data from…
The Erd\H{o}s-Ginzburg-Ziv theorem states that for any sequence of $2n-1$ integers, there exists a subsequence of $n$ elements whose sum is divisible by $n$. In this article, we provide a simple, practical $O(n\log\log n)$ algorithm and a…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…