相关论文: On Algorithms and Complexity for Sets with Cardina…

Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…

Traditionally, clustering algorithms focus on partitioning the data into groups of similar instances. The similarity objective, however, is not sufficient in applications where a fair-representation of the groups in terms of protected…

In recent years, there has been increasing interest in explanation methods for neural model predictions that offer precise formal guarantees. These include abductive (respectively, contrastive) methods, which aim to compute minimal subsets…

We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…

We study the parameterized complexity of a broad class of problems called "local graph partitioning problems" that includes the classical fixed cardinality problems as max k-vertex cover, k-densest subgraph, etc. By developing a technique…

Maximizing monotone submodular functions under cardinality constraints is a classic optimization task with several applications in data mining and machine learning. In this paper we study this problem in a dynamic environment with…

Many fundamental problems in artificial intelligence, knowledge representation, and verification involve reasoning about sets and relations between sets and can be modeled as set constraint satisfaction problems (set CSPs). Such problems…

Difference constraints have been used for termination analysis in the literature, where they denote relational inequalities of the form x' <= y + c, and describe that the value of x in the current state is at most the value of y in the…

This survey aims at demonstrating that the structure of precedence constraints plays a tremendous role on the complexity of scheduling problems. Indeed many problems can be NP-hard when considering general precedence constraints, while they…

Computational models typically assume that operations are applied in a fixed sequential order. In recent years several works have looked at relaxing this assumption, considering computations without any fixed causal structure and showing…

A kernelization algorithm for a computational problem is a procedure which compresses an instance into an equivalent instance whose size is bounded with respect to a complexity parameter. For the Boolean satisfiability problem (SAT), and…

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…

We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…

Recent works have shown that tokenisation is NP-complete. However, these works assume tokenisation is applied to inputs with unboundedly large alphabets -- an unrealistic assumption, given that in practice tokenisers operate over fixed-size…

Constraint satisfaction problems have been studied in numerous fields with practical and theoretical interests. In recent years, major breakthroughs have been made in a study of counting constraint satisfaction problems (or #CSPs). In…

We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type…

Constraint Satisfaction Problem on finite sets is known to be NP-complete in general but certain restrictions on the constraint language can ensure tractability. It was proved that if a constraint language has a weak near unanimity…

We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different…

We produce a class of $\omega$-categorical structures with finite signature by applying a model-theoretic construction -- a refinement of the Hrushosvki-encoding -- to $\omega$-categorical structures in a possibly infinite signature. We…

Kernelization---a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems---plays a central role in parameterized complexity and has triggered an extensive line of research. This is in part due to a…