Related papers: Enumeration Order complexity Equivalency
Traditional algorithm analysis treats all basic operations as equally costly, which hides significant differences in time, energy consumption, and cost between different types of computations on modern processors. We propose a…
We study the problem of generating monomials of a polynomial in the context of enumeration complexity. In this setting, the complexity measure is the delay between two solutions and the total time. We present two new algorithms for…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
Complexity theory can be viewed as the study of the relationship between computation and applications, understood the former as complexity classes and the latter as problems. Completeness results are clearly central to that view. Many…
A collection of objects, some of which are good and some are bad, is to be divided fairly among agents with different tastes, modeled by additive utility functions. If the objects cannot be shared, so that each of them must be entirely…
The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…
We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…
To determine if two lists of numbers are the same set, we sort both lists and see if we get the same result. The sorted list is a canonical form for the equivalence relation of set equality. Other canonical forms arise in graph isomorphism…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
Data from different sources rarely conform to a single formatting even if they describe the same set of entities, and this raises concerns when data from multiple sources must be joined or cross-referenced. Such a formatting mismatch is…
Graphs are extremely versatile and ubiquitous mathematical structures with potential to model a wide range of domains. For this reason, graph problems have been of interest since the early days of computer science. Some of these problems…
A new mathematical notation is proposed for the iteration of functions. It facilitates the application of the iteration of functions in mathematical and logical expressions, definitions of sets, and formulations of algorithms. Illustrations…
In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction.…
First-order learning involves finding a clause-form definition of a relation from examples of the relation and relevant background information. In this paper, a particular first-order learning system is modified to customize it for finding…
Biclustering has proved to be a powerful data analysis technique due to its wide success in various application domains. However, the existing literature presents efficient solutions only for enumerating maximal biclusters with constant…
Linked lists have long served as a valuable teaching tool in programming. However, the question arises: Are they truly practical for everyday program use? In most cases, it appears that array-based data structures offer distinct advantages,…
We study the permutation complexity of finite-state stationary stochastic processes based on a duality between values and orderings between values. First, we establish a duality between the set of all words of a fixed length and the set of…
This chapter serves as an introduction to systems engineering focused on the broad issues surrounding realizing complex integrated systems. What is a system? We pose a number of possible definitions and perspectives, but leave open the…
We study theta-joins in general and join predicates with conjunctions and disjunctions of inequalities in particular, focusing on ranked enumeration where the answers are returned incrementally in an order dictated by a given ranking…
quest for processing speed potential. In fact, we always get a fraction of the technically available computing power (so-called {\em theoretical peak}), and the gap is likely to go hand-to-hand with the hardware complexity of the target…