Related papers: A linear-time algorithm for the maximum-area inscr…

A graph is $k$-degenerate if any induced subgraph has a vertex of degree at most $k$. In this paper we prove new algorithms for cliques and similar structures for these graphs. We design linear time Fixed-Parameter Tractable algorithms for…

Knapsack is one of the most fundamental problems in theoretical computer science. In the $(1 - \epsilon)$-approximation setting, although there is a fine-grained lower bound of $(n + 1 / \epsilon) ^ {2 - o(1)}$ based on the $(\min,…

Let {\alpha} be the maximal value such that the product of an n x n^{\alpha} matrix by an n^{\alpha} x n matrix can be computed with n^{2+o(1)} arithmetic operations. In this paper we show that \alpha>0.30298, which improves the previous…

We give an overview of theoretical and practical aspects of finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of n points in the plane. Both problems are known to be NP-hard and were the…

We study the problem of computing the \textsc{Maxima} of a set of $n$ $d$-dimensional points. For dimensions 2 and 3, there are algorithms to solve the problem with order-oblivious instance-optimal running time. However, in higher…

We propose a new refinement algorithm to generate size-optimal quality-guaranteed Delaunay triangulations in the plane. The algorithm takes $O(n \log n + m)$ time, where $n$ is the input size and $m$ is the output size. This is the first…

We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…

This paper considers the problem of finding maximum volume (axis-aligned) inscribed boxes in a compact convex set, defined by a finite number of convex inequalities, and presents optimization and geometric approaches for solving them.…

Consider an n-vertex graph G = (V,E) of maximum degree Delta, and suppose that each vertex v \in V hosts a processor. The processors are allowed to communicate only with their neighbors in G. The communication is synchronous, i.e., it…

We present an algorithm to find an {\it Euclidean Shortest Path} from a source vertex $s$ to a sink vertex $t$ in the presence of obstacles in $\Re^2$. Our algorithm takes $O(T+m(\lg{m})(\lg{n}))$ time and $O(n)$ space. Here, $O(T)$ is the…

We consider the classic problem of computing the Longest Common Subsequence (LCS) of two strings of length $n$. While a simple quadratic algorithm has been known for the problem for more than 40 years, no faster algorithm has been found…

Dang et al. have given an algorithm that can find a Tarski fixed point in a $k$-dimensional lattice of width $n$ using $O(\log^{k} n)$ queries. Multiple authors have conjectured that this algorithm is optimal [Dang et al., Etessami et al.],…

We give polynomial-time dynamic-programming algorithms finding the areas of words in the presentations $\langle a, b \mid a, b \rangle$ and $\langle a, b \mid a^k, b^k; \ k \in \mathbb{N} \rangle$ of the trivial group. In the first of these…

The Maximum Induced Matching problem asks to find the maximum $k$ such that, given a graph $G=(V,E)$, can we find a subset of vertices $S$ of size $k$ for which every vertices $v$ in the induced graph $G[S]$ has exactly degree $1$. In this…

In this paper, we show $O(1.415^n)$-time and $O(1.190^n)$-space exact algorithms for 0-1 integer programs where constraints are linear equalities and coefficients are arbitrary real numbers. Our algorithms are quadratically faster than…

We study the problem of assigning non-overlapping geometric objects centered at a given set of points such that the sum of area covered by them is maximized. If the points are placed on a straight-line and the objects are disks, then the…

We analyze the correctness of an O(n log n) time divide-and-conquer algorithm for the convex hull problem when each input point is a location determined by a normal distribution. We show that the algorithm finds the convex hull of such…

In this paper we present an O(n log n) algorithm for finding a maximum flow in a directed planar graph, where the vertices are subject to capacity constraints, in addition to the arcs. If the source and the sink are on the same face, then…

Let $P$ be a set of $n$ points in the plane. We show how to find, for a given integer $k>0$, the smallest-area axis-parallel rectangle that covers $k$ points of $P$ in $O(nk^2 \log n+ n\log^2 n)$ time. We also consider the problem of, given…

For a polyhedron $P$ in $\mathbb{R}^d$, denote by $|P|$ its combinatorial complexity, i.e., the number of faces of all dimensions of the polyhedra. In this paper, we revisit the classic problem of preprocessing polyhedra independently so…