Related papers: Plantinga-Vegter algorithm takes average polynomia…
In the pairwise weighted spanner problem, the input consists of an $n$-vertex-directed graph, where each edge is assigned a cost and a length. Given $k$ vertex pairs and a distance constraint for each pair, the goal is to find a…
In Defective Coloring we are given a graph $G = (V, E)$ and two integers $\chi_d, \Delta^*$ and are asked if we can partition $V$ into $\chi_d$ color classes, so that each class induces a graph of maximum degree $\Delta^*$. We investigate…
An ortho-polygon visibility representation $\Gamma$ of a $1$-plane graph $G$ (OPVR of $G$) is an embedding preserving drawing that maps each vertex of $G$ to a distinct orthogonal polygon and each edge of $G$ to a vertical or horizontal…
Dynamic programming on path and tree decompositions of graphs is a technique that is ubiquitous in the field of parameterized and exponential-time algorithms. However, one of its drawbacks is that the space usage is exponential in the…
In the constrained planarity setting, we ask whether a graph admits a planar drawing that additionally satisfies a given set of constraints. These constraints are often derived from very natural problems; prominent examples are Level…
We consider a recently introduced fair repetitive scheduling problem involving a set of clients, each asking for their associated job to be daily scheduled on a single machine across a finite planning horizon. The goal is to determine a job…
We present PV-OSIMr, an efficient algorithm for computing the Delassus matrix (also known as the inverse operational space inertia matrix) for a kinematic tree, with the lowest order computational complexity known in literature. PV-OSIMr is…
We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…
We construct a family of root-finding algorithms which exploit the branched covering structure of a polynomial of degree $d$ with a path-lifting algorithm for finding individual roots. In particular, the family includes an algorithm that…
The three-in-a-tree problem asks for an induced tree of the input graph containing three mandatory vertices. In 2006, Chudnovsky and Seymour [Combinatorica, 2010] presented the first polynomial time algorithm for this problem, which has…
We consider the task of detecting a hidden bipartite subgraph in a given random graph. This is formulated as a hypothesis testing problem, under the null hypothesis, the graph is a realization of an Erd\H{o}s-R\'{e}nyi random graph over $n$…
We present a probabilistic Las Vegas algorithm for computing the local zeta function of a hyperelliptic curve of genus $g$ defined over $\mathbb{F}_q$. It is based on the approaches by Schoof and Pila combined with a modeling of the…
In any attempt at designing an efficient algorithm for the minimum vertex cover problem, obtaining good upper and lower bounds for the vertex cover number could be crucial. In this article we present a modified greedy algorithm of…
We generalize the recent work of S. Fomin and G. Mikhalkin on polynomial formulas for Severi degrees. The degree of the Severi variety of plane curves of degree d and delta nodes is given by a polynomial in d, provided delta is fixed and d…
We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…
In the longest plane spanning tree problem, we are given a finite planar point set $\mathcal{P}$, and our task is to find a plane (i.e., noncrossing) spanning tree for $\mathcal{P}$ with maximum total Euclidean edge length. Despite more…
In the Wishart model for sparse PCA we are given $n$ samples $Y_1,\ldots, Y_n$ drawn independently from a $d$-dimensional Gaussian distribution $N({0, Id + \beta vv^\top})$, where $\beta > 0$ and $v\in \mathbb{R}^d$ is a $k$-sparse unit…
It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using $(s\,d)^{O(n)}$ arithmetic operations, where $n$ and $s$ are the numbers of…
We consider a natural generalization of classical scheduling problems in which using a time unit for processing a job causes some time-dependent cost which must be paid in addition to the standard scheduling cost. We study the scheduling…
Evaluation complexity for convexly constrained optimization is considered and it is shown first that the complexity bound of $O(\epsilon^{-3/2})$ proved by Cartis, Gould and Toint (IMAJNA 32(4) 2012, pp.1662-1695) for computing an…