22 problems

A digraph CSP is a constraint satisfaction problem whose fixed template is a directed graph. Solvability by the few subpowers algorithm is the algorithmic property described in the…

Let $k$ be a finite field with $|k|=q$, let $X$ be a set of state transition pairs, and let $M_X$ be the associated monomial ideal with generating set $W$. A monomial tree is the d…

Let $x_i$ be objects with admissible program sets $\mathcal{P}(x_i)$, let $u\in\mathcal{P}(x_i)$ satisfy $U(u)=x_i$, and let $\hat K$ denote the estimated description-length comple…

Let $N$ denote the image resolution, and let $q$ satisfy … An iterative algorithm for inverting the ADRT with computational work of order $\mathcal{O}(N^2\log^q N)$ could exist, an…

Let $m$ and $m'$ be multicurves on the four-holed sphere, and let $\det$ denote half their intersection number. Adjusted Euclidean algorithm complexity conjecture. The adjusted Euc…

For a matrix or frame $U$ with prefix-set parameters $\rho_{T_k}(U)$, let $\rho$ and $\frac{\hat{z}_{\max}}{\hat{z}_{\min}}$ denote the corresponding parameters and output spread f…

Let $T$ be a tree with Fitch-labeling $ambda$, and let $G$ and $l$ be the network and labeling produced by Algorithm. For each transfer edge of $G$, remove the edge and any resulti…

Let $m$ be the number of labels, and let Algorithm be the algorithm described in the paper for checking combinations of pairwise label preferences and finding…

Let $kappa>0$ and let the symmetric binary perceptron (SBP) have constraint density $alpha$. A search algorithm is stable when it satisfies the stability notion used in the paper.…

Consider the symmetric binary perceptron (SBP) at a positive subcritical density, where its solution space consists mostly of totally frozen isolated solutions. A cluster is a coll…

Safe-set algorithm conjecture. There exists a polynomial-time algorithm to find a minimum safe set in a clique acyclic digraph with a constant independence number $\alpha$.

The LP-Newton methods considered here operate on a linear program and use subroutines to find nearest points in the relevant geometric sets. Polynomial-time subroutine conjecture.…

A proper interval graph $G$ has an ordering of its vertices by interval endpoints in which the relevant blocks and tuples can be represented as described. For an integer $k>2$, con…

Transfer conjecture. Provable complexity bounds for distance verification should also carry over to these more advanced techniques when applied to LDPC codes.

The graph-theoretic construction produces graphs from principal systems of blocks and uses the graph-isomorphism algorithm to compute intersections of the corresponding wreath prod…

Linear-time projection conjecture. Fast median-finding ideas could reduce the complexity of this projection from $\mathcal{O}(d\log d)$ to $\mathcal{O}(d)$ in theory, matching the…

Let $w$ be a binary word, and let ${\sc MemberPN}(w)$ be the proposed membership tester that applies the two linear-time rejection tests followed by a quadratic-time prefix-normali…

Let $M$ be the set of binary strings not rejected by the first, linear-time phase of the proposed two-phase membership tester for prefix normal words. The first phase is assumed to…

Let $L_0$ denote the relevant geometric walk-length parameter and let $omega_n$ denote the paper's parameter controlling the random Delaunay triangulation. The algorithm…

Consider the accelerated versions of the IRWA and ADAL algorithms for the exact penalty subproblem, and let an $varepsilon$-optimal solution mean a solution whose objective value i…

Guruswami–Sudan interpolation amounts to solving a structured linear system of equations, and reduced systems can be obtained using re-encoding, Sierpinski, or combined prefactors.…

Let $n$ be the number of tetrahedra and let $k'$ denote the size of the standard solution set produced by Algorithm for converting a quadrilateral solution set to a standard soluti…