Related papers: An Atomic Viewpoint of the TP Completion Problem
A topologized semilattice $X$ is called complete if each non-empty chain $C\subset X$ has $\inf C$ and $\sup C$ that belong to the closure $C$ of the chain $C$ in $X$. In this paper, we introduce various concepts of completeness of…
We present a new problem called the incomplete Traveling Tournament problem, which introduces the well known Traveling Tournament Problem into the realm of incomplete round-robin tournaments. We focus on the case where teams can face each…
We investigate the problem of completing partial matrices to rank-one matrices in the standard simplex. The motivation for studying this problem comes from statistics: A lack of eligible completion can provide a falsification test for…
We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…
Three algorithms are presented that determine the existence of satisfying assignments for 3SAT Boolean satisfiability expressions. One algorithm is presented for determining an instance of a satisfying assignment, where such exists. The…
Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in…
Let ${\cal F}$ be a family of graphs. In the ${\cal F}$-Completion problem, we are given a graph $G$ and an integer $k$ as input, and asked whether at most $k$ edges can be added to $G$ so that the resulting graph does not contain a graph…
Quantum entanglement is a particularly useful characterization of topological orders which lack conventional order parameters. In this work, we study the entanglement in topologically ordered states between two arbitrary spatial regions,…
In a previous paper we have presented a CEGAR approach for the verification of parameterized systems with an arbitrary number of processes organized in an array or a ring. The technique is based on the iterative computation of parameterized…
Let G = (V, E) be a directed acyclic graph with two distinguished vertices s, t and let F be a set of forbidden pairs of vertices. We say that a path in G is safe, if it contains at most one vertex from each pair {u, v} in F. Given G and F,…
Using the matrix product state (MPS) representation of tensor train decompositions, in this paper we propose a tensor completion algorithm which alternates over the matrices (tensors) in the MPS representation. This development is motivated…
Mathematical programs with vanishing constraints (MPVCs) are a class of nonlinear optimization problems with applications to various engineering problems such as truss topology design and robot motion planning. MPVCs are difficult problems…
Several works have recently investigated the parameterized complexity of data completion problems, motivated by their applications in machine learning, and clustering in particular. Interestingly, these problems can be equivalently…
The problem of matrix completion and decomposition in the cone of positive semidefinite (PSD) matrices is a well-understood problem, with many important applications in areas such as linear algebra, optimization, and control theory. This…
A type system combining type application, constants as types, union types (associative, commutative and idempotent) and recursive types has recently been proposed for statically typing path polymorphism, the ability to define functions that…
Background: A classical problem in metabolic design is to maximize the production of desired compound in a given chemical reaction network by appropriately directing the mass flow through the network. Computationally, this problem is…
We introduce a new decision problem, called Packed Interval Covering (PIC) and show that it is NP-complete.
We show that reachability, repeated reachability, nontermination and unboundedness are NP-complete for Lossy Channel Machines that are flat, i.e., with no nested cycles in the control graph. The upper complexity bound relies on a fine…
Alternating timed automata (ATA) are an extension of timed automata, that are closed under complementation and hence amenable to logic-to-automata translations. Several timed logics, including Metric Temporal Logic (MTL), can be converted…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…