Related papers: Approximately counting maximal independent set is …
Boolean satisfiability ({\SAT}) has played a key role in diverse areas spanning testing, formal verification, planning, optimization, inferencing and the like. Apart from the classical problem of checking boolean satisfiability, the…
Model counting ($\#\text{SAT}$) is a fundamental yet $\#\text{P}$-complete problem central to probabilistic reasoning. In this work, we address \textit{incremental model counting}, where sequences of structurally similar formulas must be…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
The goal of this paper is to understand the complexity of symmetry breaking problems, specifically maximal independent set (MIS) and the closely related $\beta$-ruling set problem, in two computational models suited for large-scale graph…
Sum-product networks (SPNs) are a class of probabilistic graphical models that allow tractable marginal inference. However, the maximum a posteriori (MAP) inference in SPNs is NP-hard. We investigate MAP inference in SPNs from both…
In this paper, we present a novel MaxSAT-based technique to compute Maximum Probability Minimal Cut Sets (MPMCSs) in fault trees. We model the MPMCS problem as a Weighted Partial MaxSAT problem and solve it using a parallel SAT-solving…
The paper considers the problem of finding the largest possible set P(n), a subset of the set N of the natural numbers, with the property that a number is in P(n) if and only if it is a sum of n distinct naturals all in P(n) or none in…
A powerful technique for solving combinatorial optimization problems is to reduce the search space without compromising the solution quality by exploring intrinsic mathematical properties of the problems. For the maximum weight independent…
In 1973, Katona raised the problem of determining the maximum number of subsets in a separating cover on n elements. The answer to Katona's question turns out to be the inverse to the answer to a much simpler question: what is the largest…
The maximization for the independence systems defined on graphs is a generalization of combinatorial optimization problems such as the maximum $b$-matching, the unweighted MAX-SAT, the matchoid, and the maximum timed matching problems. In…
Inverse optimization is the problem of determining the values of missing input parameters for an associated forward problem that are closest to given estimates and that will make a given target vector optimal. This study is concerned with…
Given a family of subsets $\mathcal S$ over a set of elements~$X$ and two integers~$p$ and~$k$, Max k-Set Cover consists of finding a subfamily~$\mathcal T \subseteq \mathcal S$ of cardinality at most~$k$, covering at least~$p$ elements…
Inspired by the developments in quantum computing, building domain-specific classical hardware to solve computationally hard problems has received increasing attention. Here, by introducing systematic sparsification techniques, we…
A set of graphs is said to be independent if there is no homomorphism between distinct graphs from the set. We consider the existence problems related to the independent sets of countable graphs. While the maximal size of an independent set…
We resolve the longstanding open problem concerning the computational complexity of Max Cut on interval graphs by showing that it is NP-complete.
An independent dominating set of a graph, also known as a maximal independent set, is a set $S$ of pairwise non-adjacent vertices such that every vertex not in $S$ is adjacent to some vertex in $S$. We prove that for $\Delta=4$ or…
The Maximum Weight Independent Set problem is a fundamental NP-hard problem in combinatorial optimization with several real-world applications. Given an undirected vertex-weighted graph, the problem is to find a subset of the vertices with…
Using well-known mathematical problems for encryption is a widely used technique because they are computationally hard and provide security against potential attacks on the encryption method. The subset sum problem (SSP) can be defined as…
The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of…
We present fully dynamic approximation algorithms for the Maximum Independent Set problem on several types of geometric objects: intervals on the real line, arbitrary axis-aligned squares in the plane and axis-aligned $d$-dimensional…