Related papers: Algorithms for Covering Multiple Barriers
The problem of listing the $K$ shortest simple (loopless) $st$-paths in a graph has been studied since the early 1960s. For a non-negatively weighted graph with $n$ vertices and $m$ edges, the most efficient solution is an $O(K(mn + n^2…
The coverage problem in wireless sensor networks deals with the problem of covering a region or parts of it with sensors. In this paper, we address the problem of covering a set of line segments in sensor networks. A line segment ` is said…
We describe the first nearly linear-time approximation algorithms for explicitly given mixed packing/covering linear programs, and for (non-metric) fractional facility location. We also describe the first parallel algorithms requiring only…
In this paper, we first consider the subpath convex hull query problem: Given a simple path $\pi$ of $n$ vertices, preprocess it so that the convex hull of any query subpath of $\pi$ can be quickly obtained. Previously, Guibas, Hershberger,…
We study the complexity of a fundamental algorithm for fairly allocating indivisible items, the round-robin algorithm. For $n$ agents and $m$ items, we show that the algorithm can be implemented in time $O(nm\log(m/n))$ in the worst case.…
In this note, we give an algorithm that computes the linearwidth of input $n$-vertex graphs in time $O^*(2^n)$, which improves a trivial $O^*(2^m)$-time algorithm, where $n$ and $m$ the number of vertices and edges, respectively.
We introduce space-efficient plane-sweep algorithms for basic planar geometric problems. It is assumed that the input is in a read-only array of $n$ items and that the available workspace is $\Theta(s)$ bits, where $\lg n \leq s \leq n…
We consider the problem of scheduling communication on optical WDM (wavelength division multiplexing) networks using the light-trails technology. We seek to design scheduling algorithms such that the given transmission requests can be…
Consider a pair of plane straight-line graphs, whose edges are colored red and blue, respectively, and let n be the total complexity of both graphs. We present a O(n log n)-time O(n)-space technique to preprocess such pair of graphs, that…
We study graph connectivity problem in MPC model. On an undirected graph with $n$ nodes and $m$ edges, $O(\log n)$ round connectivity algorithms have been known for over 35 years. However, no algorithms with better complexity bounds were…
We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an…
We give a deterministic $O(m\log^{2/3}n)$-time algorithm for single-source shortest paths (SSSP) on directed graphs with real non-negative edge weights in the comparison-addition model. This is the first result to break the $O(m+n\log n)$…
We study the influence of a graph parameter called modular-width on the time complexity for optimally solving well-known polynomial problems such as Maximum Matching, Triangle Counting, and Maximum $s$-$t$ Vertex-Capacitated Flow. The…
We show how to construct an overlay network of constant degree and diameter $O(\log n)$ in time $O(\log n)$ starting from an arbitrary weakly connected graph. We assume a synchronous communication network in which nodes can send messages to…
We provide a new algorithm to determine stuttering equivalence with time complexity $O(m \log n)$, where $n$ is the number of states and $m$ is the number of transitions of a Kripke structure. This algorithm can also be used to determine…
A set of points and a positive integer $m$ are given and our goal is to cover the maximum number of these point with $m$ disks. We devise the first output sensitive algorithm for this problem. We introduce a parameter $\rho$ as the maximum…
We give an iterative algorithm for finding the maximum flow between a set of sources and sinks that lie on the boundary of a planar graph. Our algorithm uses only O(n) queries to simple data structures, achieving an O(n log n) running time…
In 2013, Orlin proved that the max flow problem could be solved in $O(nm)$ time. His algorithm ran in $O(nm + m^{1.94})$ time, which was the fastest for graphs with fewer than $n^{1.06}$ arcs. If the graph was not sufficiently sparse, the…
Branching bisimilarity is a behavioural equivalence relation on labelled transition systems that takes internal actions into account. It has the traditional advantage that algorithms for branching bisimilarity are more efficient than all…
We revisit a fundamental problem in string matching: given a pattern of length m and a text of length n, both over an alphabet of size $\sigma$, compute the Hamming distance between the pattern and the text at every location. Several…