相关论文: Alphabetic Coding with Exponential Costs

Binary optimisation tasks are ubiquitous in areas ranging from logistics to cryptography. The exponential complexity of such problems means that the performance of traditional computational methods decreases rapidly with increasing problem…

Many optimization techniques evaluate solutions consecutively, where the next candidate for evaluation is determined by the results of previous evaluations. For example, these include iterative methods, "black box" optimization algorithms,…

Adaptive binary search trees are a fundamental data structure for organizing hierarchical information. Their ability to dynamically adjust to access patterns makes them particularly valuable for building responsive and efficient networked…

A number of recent works have employed decision trees for the construction of explainable partitions that aim to minimize the $k$-means cost function. These works, however, largely ignore metrics related to the depths of the leaves in the…

In this paper we present novel algorithmic techniques with a O(H(N)+N/H(N)) time complexity for performing several types of queries and updates on general rooted trees, binary search trees and lists of size N. For rooted trees we introduce…

The minimum-cost arborescence problem is a well-studied problem in the area of graph theory, with known polynomial-time algorithms for solving it. Previous literature introduced new variations on the original problem with different…

Large Language Models (LLMs) have achieved significant advances in reasoning tasks. A key approach is tree-based search with verifiers, which expand candidate reasoning paths and use reward models to guide pruning and selection. Although…

The problem of rectangle tiling binary arrays is defined as follows. Given an $n \times n$ array $A$ of zeros and ones and a natural number $p$, our task is to partition $A$ into at most $p$ rectangular tiles, so that the maximal weight of…

Hierarchical clustering is a critical task in numerous domains. Many approaches are based on heuristics and the properties of the resulting clusterings are studied post hoc. However, in several applications, there is a natural cost function…

We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…

We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of $k$ solutions. This approach is appropriate for decision problems under uncertainty where the…

Allocating physical layer resources to users based on channel quality, buffer size, requirements and constraints represents one of the central optimization problems in the management of radio resources. The solution space grows…

Solution techniques for Constraint Satisfaction and Optimisation Problems often make use of backtrack search methods, exploiting variable and value ordering heuristics. In this paper, we propose and analyse a very simple method to apply in…

Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and…

We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a…

Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small…

Integrated interpretability without sacrificing the prediction accuracy of decision making algorithms has the potential of greatly improving their value to the user. Instead of assigning a label to an image directly, we propose to learn…

The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…

In binary polynomial optimization, the goal is to find a binary point maximizing a given polynomial function. In this paper, we propose a novel way of formulating this general optimization problem, which we call factorized binary polynomial…

In blackbox optimization, evaluation of the objective and constraint functions is time consuming. In some situations, constraint values may be evaluated independently or sequentially. The present work proposes and compares two strategies to…