Related papers: Algorithmic Structure in Subset Sum: Deterministic…
The constraint satisfaction problems k-SAT and Quantum k-SAT (k-QSAT) are canonical NP-complete and QMA_1-complete problems (for k>=3), respectively, where QMA_1 is a quantum generalization of NP with one-sided error. Whereas k-SAT has been…
From a theoretical point of view, finding the solution set of a system of inequalities in only two variables is easy. However, if we want to get rigorous bounds on this set with floating point arithmetic, in all possible cases, then things…
Unbounded SubsetSum is a classical textbook problem: given integers $w_1,w_2,\cdots,w_n\in [1,u],~c,u$, we need to find if there exists $m_1,m_2,\cdots,m_n\in \mathbb{N}$ satisfying $c=\sum_{i=1}^n w_im_i$. In its all-target version, $t\in…
The goal of this paper is to set a constraint programming framework to solve lot-sizing problems. More specifically, we consider a single-item lot-sizing problem with time-varying lower and upper bounds for production and inventory. The…
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…
This paper develops a measure for bounding the performance of AND/OR search algorithms for solving a variety of queries over graphical models. We show how drawing a connection to the recent notion of hypertree decompositions allows to…
Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…
Knapsack and Partition are two important additive problems whose fine-grained complexities in the $(1-\varepsilon)$-approximation setting are not yet settled. In this work, we make progress on both problems by giving improved algorithms. -…
Handling an infinite number of inequality constraints in infinite-dimensional spaces occurs in many fields, from global optimization to optimal transport. These problems have been tackled individually in several previous articles through…
Even if path planning can be solved using standard techniques from dynamic programming and control, the problem can also be approached using probabilistic inference. The algorithms that emerge using the latter framework bear some appealing…
We introduce and study four optimization problems that generalize the well-known subset sum problem. Given a node-weighted digraph, select a subset of vertices whose total weight does not exceed a given budget. Some additional constraints…
Majority-SAT is the problem of determining whether an input $n$-variable formula in conjunctive normal form (CNF) has at least $2^{n-1}$ satisfying assignments. Majority-SAT and related problems have been studied extensively in various AI…
Assisted by the availability of data and high performance computing, deep learning techniques have achieved breakthroughs and surpassed human performance empirically in difficult tasks, including object recognition, speech recognition, and…
Although recent provable methods have been developed to compute preimage bounds for neural networks, their scalability is fundamentally limited by the #P-hardness of the problem. In this work, we adopt a novel probabilistic perspective,…
Feature subset selection, as a special case of the general subset selection problem, has been the topic of a considerable number of studies due to the growing importance of data-mining applications. In the feature subset selection problem…
The feasibility-seeking approach provides a systematic scheme to manage and solve complex constraints for continuous problems, and we explore it for the floorplanning problems with increasingly heterogeneous constraints. The classic…
Detection of symmetry is vital to problem solving. Most of the problems of computer vision and computer graphics and machine intelligence in general, can be reduced to symmetry detection problem. Unstructured search problem can also be…
In this paper, we study the "sum composition problem" between two lists $A$ and $B$ of positive integers. We start by saying that $B$ is "sum composition" of $A$ when there exists an ordered $m$-partition $[A_1,\ldots,A_m]$ of $A$ where $m$…
This paper presents a complete algorithmic study of the decision Boolean Satisfiability Problem under the classical computation and quantum computation theories. The paper depicts deterministic and probabilistic algorithms, propositions of…
The modular subset sum problem consists of deciding, given a modulus $m$, a multiset $S$ of $n$ integers in $0..m-1$, and a target integer $t$, whether there exists a subset of $S$ with elements summing to $t \mod m $, and to report such a…