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We consider a classical scheduling problem on $m$ identical machines. For an arbitrary constant $q>1$, the aim is to assign jobs to machines such that $\sum_{i=1}^m C_i^q$ is minimized, where $C_i$ is the total processing time of jobs…
Given $n$ intervals on a line $\ell$, we consider the problem of moving these intervals on $\ell$ such that no two intervals overlap and the maximum moving distance of the intervals is minimized. The difficulty for solving the problem lies…
A modified form of Euclid's algorithm has gained popularity among musical composers following Toussaint's 2005 survey of so-called Euclidean rhythms in world music. We offer a method to easily calculate Euclid's algorithm by hand as a…
An experimental comparison of two or more optimization algorithms requires the same computational resources to be assigned to each algorithm. When a maximum runtime is set as the stopping criterion, all algorithms need to be executed in the…
This paper reports about the development of two provably correct approximate algorithms which calculate the Euclidean shortest path (ESP) within a given cube-curve with arbitrary accuracy, defined by $\epsilon >0$, and in time complexity…
To improve our understanding of connected systems, different tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the graph comparison…
We study exact algorithms for Euclidean TSP in $\mathbb{R}^d$. In the early 1990s algorithms with $n^{O(\sqrt{n})}$ running time were presented for the planar case, and some years later an algorithm with $n^{O(n^{1-1/d})}$ running time was…
Theory of evolutionary computation (EC) aims at providing mathematically founded statements about the performance of evolutionary algorithms (EAs). The predominant topic in this research domain is runtime analysis, which studies the time it…
One of the most important quantum algorithms ever discovered is Grover's algorithm for searching an unordered set. We give a new lower bound in the query model which proves that Grover's algorithm is exactly optimal. Similar to existing…
We present a new algorithm for computing upper bounds on the number of executions of each program instruction during any single program run. The upper bounds are expressed as functions of program input values. The algorithm is primarily…
It is well-known that the Ford-Fulkerson algorithm for finding a maximum flow in a network need not terminate if we allow the arc capacities to take irrational values. Every non-terminating example converges to a limit flow, but this limit…
We revisit the classic task of finding the shortest tour of $n$ points in $d$-dimensional Euclidean space, for any fixed constant $d \geq 2$. We determine the optimal dependence on $\varepsilon$ in the running time of an algorithm that…
It has been recently reported that classical systems have speed limit for state evolution, although such a concept of speed limit had been considered to be unique to quantum systems. Owing to the speed limit for classical system, the lower…
We study sublinear time algorithms for estimating the size of maximum matching in graphs. Our main result is a $(\frac{1}{2}+\Omega(1))$-approximation algorithm which can be implemented in $O(n^{1+\epsilon})$ time, where $n$ is the number…
We show that any one-counter automaton with $n$ states, if its language is non-empty, accepts some word of length at most $O(n^2)$. This closes the gap between the previously known upper bound of $O(n^3)$ and lower bound of $\Omega(n^2)$.…
This study examines the time complexities of the unbalanced optimal transport problems from an algorithmic perspective for the first time. We reveal which problems in unbalanced optimal transport can/cannot be solved efficiently.…
This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…
The problem of finding the longest simple cycle in a directed graph is NP-hard, with critical applications in computational biology, scheduling, and network analysis. Existing approaches include exact algorithms with exponential runtimes,…
All known algorithms for the Fr\'echet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; second, they use this oracle to find the optimum from a finite set of critical values.…
Understanding how evolutionary algorithms perform on constrained problems has gained increasing attention in recent years. In this paper, we study how evolutionary algorithms optimize constrained versions of the classical LeadingOnes…