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We prove that the exact versions of the domatic number problem are complete for the levels of the boolean hierarchy over NP. The domatic number problem, which arises in the area of computer networks, is the problem of partitioning a given…
Consider a fluid flowing through a junction between two pipes with different sections. Its evolution is described by the 2D or 3D Euler equations, whose analytical theory is far from complete and whose numerical treatment may be rather…
Large language models have demonstrated remarkable capabilities across many tasks, yet face significant challenges when dealing with recursive reasoning problems, those requiring the resolution of nested hierarchical structures. While prior…
Estimating the discrepancy of the hypergraph of all arithmetic progressions in the set $[N]=\{1,2,\hdots,N\}$ was one of the famous open problems in combinatorial discrepancy theory for a long time. An extension of this classical hypergraph…
Given a directed graph $G = (V, E)$, the $k$-path partition problem is to find a minimum collection of vertex-disjoint directed paths each of order at most $k$ to cover all the vertices of $V$. The problem has various applications in…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
An invariant differential-geometric approach to the integrability of (2+1)-dimensional systems of hydrodynamic type u_t+A(u)u_x+B(u)u_y=0 is developed. It is proved that the existence of special solutions known as `double waves' is…
In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
The sliding window model of computation captures scenarios in which data is arriving continuously, but only the latest $w$ elements should be used for analysis. The goal is to design algorithms that update the solution efficiently with each…
Given an inverse problem with a normalizing flow prior, we wish to estimate the distribution of the underlying signal conditioned on the observations. We approach this problem as a task of conditional inference on the pre-trained…
We reconsider the classical problem of representing a finite number of forms of degree d in n+1 variables as sums of powers of linear forms. We define a geometric construct called a `grove', which, in a number of cases allows us to…
The concept of $k$-planarity is extensively studied in the context of Beyond Planarity. A graph is $k$-planar if it admits a drawing in the plane in which each edge is crossed at most $k$ times. The local crossing number of a graph is the…
The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the…
A natural variant of the classical online $k$-server problem is the Weighted $k$-server problem, where the cost of moving a server is its weight times the distance through which it moves. Despite its apparent simplicity, the weighted…
The modified Bessel function of the second kind K$\nu$ appears in a wide variety of applied scientific fields. While its use is greatly facilitated by an implementation in most numerical libraries, overflow issues can be encountered…
Let $k\geq 2$ and $\mathcal{P} (n) = (A_1 n + B_1 ) \cdots (A_k n + B_k)$ where all the $A_i, B_i$ are integers. Suppose that $\mathcal{P} (n)$ has no fixed prime divisors. For each choice of $k$ it is known that there exists an integer…
The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take…
We consider a porous solid covered with a water film (or with a drop) in situations where the liquid is pumped in, either spontaneously (if the porous medium is hydrophilic) or mechanically (by an external pump). The dynamics of dewetting…
A determined algorithm is presented for solving the rSUM problem for any natural r with a sub-quadratic assessment of time complexity in some cases. In terms of an amount of memory used the obtained algorithm is the nlog^3(n) order. The…