Related papers: Tokenisation is NP-Complete
We present two complementary techniques called catalysis and inhibition which allow one to determine if a given pattern is TP completable or TP non-completable, respectively. Empirically, these techniques require considering only one…
In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…
We present the first formal verification of approximation algorithms for NP-complete optimization problems: vertex cover, independent set, set cover, center selection, load balancing, and bin packing. We uncover incompletenesses in existing…
Shellings of simplicial complexes have long been a useful tool in topological and algebraic combinatorics. Shellings of a complex expose a large amount of information in a helpful way, but are not easy to construct, often requiring deep…
Typically, tokenization is the very first step in most text processing works. As a token serves as an atomic unit that embeds the contextual information of text, how to define a token plays a decisive role in the performance of a model.Even…
Computational complexity of the design problem for a network with a target value of Region-Based Component Decomposition Number (RBCDN) has been proven to be NP-complete.
In this article we introduce a new complexity class called PQMA_log(2). Informally, this is the class of languages for which membership has a logarithmic-size quantum proof with perfect completeness and soundness which is polynomially close…
In this paper, we address the problem of searching for semantically similar images from a large database. We present a compact coding approach, supervised quantization. Our approach simultaneously learns feature selection that linearly…
We show that the problem of finding a set with maximum cohesion in an undirected network is NP-hard.
We study provably effective and efficient data reduction for a class of NP-hard graph modification problems based on vertex degree properties. We show fixed-parameter tractability for NP-hard graph completion (that is, edge addition) cases…
Approximating a definite integral of product of cosines to within an accuracy of n binary digits where the integrand depends on input integers x[k] given in binary radix, is equivalent to counting the number of equal-sum partitions of the…
In several different applications, including data transformation and entity resolution, rules are used to capture aspects of knowledge about the application at hand. Often, a large set of such rules is generated automatically or…
Co-clustering, that is, partitioning a numerical matrix into homogeneous submatrices, has many applications ranging from bioinformatics to election analysis. Many interesting variants of co-clustering are NP-hard. We focus on the basic…
Past research on probabilistic databases has studied the problem of answering queries on a static database. Application scenarios of probabilistic databases however often involve the conditioning of a database using additional information…
We introduce and study several notions of approximation for ontology-mediated queries based on the description logics ALC and ALCI. Our approximations are of two kinds: we may (1) replace the ontology with one formulated in a tractable…
Biclustering involves the simultaneous clustering of objects and their attributes, thus defining local two-way clustering models. Recently, efficient algorithms were conceived to enumerate all biclusters in real-valued datasets. In this…
Kernelization algorithms are polynomial-time reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. For example, d-Set Matching for integers d>2 is the problem of finding a matching of size…
This article discusses completeness of Boolean Algebra as First Order Theory in Goedel's meaning. If Theory is complete then any possible transformation is equivalent to some transformation using axioms, predicates etc. defined for this…
Subword tokenization has become the de-facto standard for tokenization, although comparative evaluations of subword vocabulary quality across languages are scarce. Existing evaluation studies focus on the effect of a tokenization algorithm…
We present two techniques novel in numerical methods. The first technique compiles the domain of the numerical methods as a discretized volume. Congruent elements are glued together to compile the domain over which the solution of a…