Related papers: Minimizing the Aggregate Movements for Interval Co…
We consider a classical k-center problem in trees. Let T be a tree of n vertices and every vertex has a nonnegative weight. The problem is to find k centers on the edges of T such that the maximum weighted distance from all vertices to…
Given a set $P$ of $n$ points and a set $S$ of $n$ segments in the plane, we consider the problem of computing for each segment of $S$ its closest point in $P$. The previously best algorithm solves the problem in $n^{4/3}2^{O(\log^*n)}$…
Consider a team of $k \leq n$ autonomous mobile robots initially placed at a node of an arbitrary graph $G$ with $n$ nodes. The dispersion problem asks for a distributed algorithm that allows the robots to reach a configuration in which…
We study a problem where k autonomous mobile agents are initially located on distinct nodes of a weighted graph (with n nodes and m edges). Each autonomous mobile agent has a predefined velocity and is only allowed to move along the edges…
We study Geometric Graph Edit Distance (GGED), a graph-editing model to compute the minimum edit distance of intersection graphs that uses moving objects as an edit operation. We first show an $O(n\log n)$-time algorithm that minimises the…
The index coding problem is concerned with broadcasting encoded information to a collection of receivers in a way that enables each receiver to discover its required data based on its side information, which comprises the data required by…
In the semi-streaming model for processing massive graphs, an algorithm makes multiple passes over the edges of a given $n$-vertex graph and is tasked with computing the solution to a problem using $O(n \cdot \text{polylog}(n))$ space.…
In this paper we present new data structures for two extensively studied variants of the orthogonal range searching problem. First, we describe a data structure that supports two-dimensional orthogonal range minima queries in $O(n)$ space…
Given an $x$-monotone polygonal chain $T$ with $n$ vertices, and an integer $k$, we consider the problem of finding the lowest horizontal line $L$ lying above $T$ with $k$ point guards lying on $L$, so that every point on the chain is…
The Planar Graph Metric Compression Problem is to compactly encode the distances among $k$ nodes in a planar graph of size $n$. Two na\"ive solutions are to store the graph using $O(n)$ bits, or to explicitly store the distance matrix with…
We consider a generalized version of the (weighted) one-center problem on graphs. Given an undirected graph $G$ of $n$ vertices and $m$ edges and a positive integer $k\leq n$, the problem aims to find a point in $G$ so that the maximum…
We present an O(n^3 log^2 n)-time algorithm for the following problem: given a finite metric space X, create a star-topology network with the points of X as its leaves, such that the distances in the star are at least as large as in X, with…
We investigate the problem of optimally assigning a large number of robots (or other types of autonomous agents) to guard the perimeters of closed 2D regions, where the perimeter of each region to be guarded may contain multiple disjoint…
This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the…
Recently, Yamazaki et al. provided an algorithm that enumerates all non-isomorphic interval graphs on $n$ vertices with an $O(n^4)$ time delay. In this paper, we improve their algorithm and achieve $O(n^3 \log n)$ time delay. We also extend…
We study an abstract optimization problem arising from biomolecular sequence analysis. For a sequence A of pairs (a_i,w_i) for i = 1,..,n and w_i>0, a segment A(i,j) is a consecutive subsequence of A starting with index i and ending with…
We consider the following distributed pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown $n$-node network. Their goal is to execute a search strategy that guarantees capturing a fast…
We consider the problem of computing a sequence of range minimum queries. We assume a sequence of commands that contains values and queries. Our goal is to quickly determine the minimum value that exists between the current position and a…
Explorable heap selection is the problem of selecting the $n$th smallest value in a binary heap. The key values can only be accessed by traversing through the underlying infinite binary tree, and the complexity of the algorithm is measured…
The maximum/minimum bisection problems are, given an edge-weighted graph, to find a bipartition of the vertex set into two sets whose sizes differ by at most one, such that the total weight of edges between the two sets is…