Related papers: Polynomial Time Local Decision Revisited
Consider any locally checkable labeling problem $\Pi$ in rooted regular trees: there is a finite set of labels $\Sigma$, and for each label $x \in \Sigma$ we specify what are permitted label combinations of the children for an internal node…
This paper solves a long standing open problem of whether NP-complete problems could be solved in polynomial time on a deterministic Turing machine by showing that the indistinguishable binomial decision tree can be formed in a 3-SAT…
This thesis provides an explanation of L\'aszl\'o Babai's quasi-polynomial algorithm for the Graph Isomorphism Problem published in 2015 with a particular focus on the case of local certificates, i.e. the case that cannot be dealt with by…
Budgeted uncertainty sets have been established as a major influence on uncertainty modeling for robust optimization problems. A drawback of such sets is that the budget constraint only restricts the global amount of cost increase that can…
Limits on the number of satisfying assignments for CNS instances with n variables and m clauses are derived from various inequalities. Some bounds can be calculated in polynomial time, sharper bounds demand information about the…
We consider combinatorial problems that can be solved in polynomial time for graphs of bounded treewidth but where the order of the polynomial that bounds the running time is expected to depend on the treewidth bound. First we review some…
Distributed networks are prone to errors so verifying their output is critical. Hence, we develop LOCAL certification protocols for graph properties in which nodes are given certificates that allow them to check whether their network as a…
Choiceless Polynomial Time (CPT) is currently the only candidate logic for capturing PTIME (that is, it is contained in PTIME and has not been separated from it). A prominent example of a decision problem in PTIME that is not known to be…
The issue of identifiers is crucial in distributed computing. Informally, identities are used for tackling two of the fundamental difficulties that areinherent to deterministic distributed computing, namely: (1) symmetry breaking, and (2)…
Given a weighted, ordered query set $Q$ and a partition of $Q$ into classes, we study the problem of computing a minimum-cost decision tree that, given any query $q$ in $Q$, uses equality tests and less-than comparisons to determine the…
A set of polynomials in noncommuting variables is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. By a theorem of Camino, Helton, Skelton and Ye, a finite locally linearly…
In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
Nowadays there are several classes of constrained codes intended for different applications. The following two large classes can be distinguished. The first class contains codes with local constraints; for example, the source data must be…
The locality of a graph problem is the smallest distance $T$ such that each node can choose its own part of the solution based on its radius-$T$ neighborhood. In many settings, a graph problem can be solved efficiently with a distributed or…
We investigate the correspondence between the time and space recognition complexity of languages. For this purpose, we will code the long-continued computations of deterministic two-tape Turing machines by the relatively short-length…
We present precise bit and degree estimates for the optimal value of the polynomial optimization problem $f^*:=\text{inf}_{x\in \mathscr{X}}~f(x)$, where $\mathscr{X}$ is a semi-algebraic set satisfying some non-degeneracy conditions. Our…
The linear induced matching width (LMIM-width) of a graph is a width parameter defined by using the notion of branch-decompositions of a set function on ternary trees. In this paper we study output-polynomial enumeration algorithms on…
In this paper, we study learning and testing decision tree of size and depth that are significantly smaller than the number of attributes $n$. Our main result addresses the problem of poly$(n,1/\epsilon)$ time algorithms with…
We study $\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on…
Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…