Related papers: On the Complexity of the CSG Tree Extraction Probl…
We study the compressed representation of a ranked tree by a (string) straight-line program (SLP) for its preorder traversal, and compare it with the well-studied representation by straight-line context free tree grammars (which are also…
This paper studies the computational complexity of disambiguation under probabilistic tree-grammars and context-free grammars. It presents a proof that the following problems are NP-hard: computing the Most Probable Parse (MPP) from a…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
The tree-depth problem can be seen as finding an elimination tree of minimum height for a given input graph $G$. We introduce a bicriteria generalization in which additionally the width of the elimination tree needs to be bounded by some…
This paper deals with computation trees over an arbitrary structure consisting of a set along with collections of functions and predicates that are defined on it. It is devoted to the comparative analysis of three parameters of problems…
In this paper, we study three algorithmic problems involving computation trees: the optimization, solvability, and satisfiability problems. The solvability problem is concerned with recognizing computation trees that solve problems. The…
This paper introduces a data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored in a trie whose nodes are in bijection with the faces of the…
Document clustering as an unsupervised approach extensively used to navigate, filter, summarize and manage large collection of document repositories like the World Wide Web (WWW). Recently, focuses in this domain shifted from traditional…
We study the computational complexity of the physical problem of finding vacua of string theory which agree with data, such as the cosmological constant, and show that such problems are typically NP hard. In particular, we prove that in the…
Hard instances of natural computational problems are often elusive. In this note we present an example of a natural decision problem, the word problem for a certain finitely presented group, whose hard instances are easy to find. More…
Clustering is a well-known and studied problem, one of its variants, called contiguity-constrained clustering, accepts as a second input a graph used to encode prior information about cluster structure by means of contiguity constraints…
The clustered planarity problem (c-planarity) asks whether a hierarchically clustered graph admits a planar drawing such that the clusters can be nicely represented by regions. We introduce the cd-tree data structure and give a new…
Given a graph $G$, the Connected Vertex Cover problem (CVC) asks to find a minimum cardinality vertex cover of $G$ that induces a connected subgraph. In this paper we describe some approaches to solve the CVC problem exactly. First, we give…
The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…
There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types…
Tree ensembles, such as random forests and boosted trees, are renowned for their high prediction performance. However, their interpretability is critically limited due to the enormous complexity. In this study, we present a method to make a…
In this paper, we introduce a set of tools for providing user-friendly explanations in an explanation-based constraint programming system. The idea is to represent the constraints of a problem as an hierarchy (a tree). Users are then…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
We consider finding a counterfactual explanation for a classification or regression forest, such as a random forest. This requires solving an optimization problem to find the closest input instance to a given instance for which the forest…
We study the problem of decomposing (clustering) a tree with respect to costs attributed to pairs of nodes, so as to minimize the sum of costs for those pairs of nodes that are in the same component (cluster). For the general case and for…