16,080 research outputs found
JGraphT -- A Java library for graph data structures and algorithms
Mathematical software and graph-theoretical algorithmic packages to
efficiently model, analyze and query graphs are crucial in an era where
large-scale spatial, societal and economic network data are abundantly
available. One such package is JGraphT, a programming library which contains
very efficient and generic graph data-structures along with a large collection
of state-of-the-art algorithms. The library is written in Java with stability,
interoperability and performance in mind. A distinctive feature of this library
is the ability to model vertices and edges as arbitrary objects, thereby
permitting natural representations of many common networks including
transportation, social and biological networks. Besides classic graph
algorithms such as shortest-paths and spanning-tree algorithms, the library
contains numerous advanced algorithms: graph and subgraph isomorphism; matching
and flow problems; approximation algorithms for NP-hard problems such as
independent set and TSP; and several more exotic algorithms such as Berge graph
detection. Due to its versatility and generic design, JGraphT is currently used
in large-scale commercial, non-commercial and academic research projects. In
this work we describe in detail the design and underlying structure of the
library, and discuss its most important features and algorithms. A
computational study is conducted to evaluate the performance of JGraphT versus
a number of similar libraries. Experiments on a large number of graphs over a
variety of popular algorithms show that JGraphT is highly competitive with
other established libraries such as NetworkX or the BGL.Comment: Major Revisio
Best of Two Local Models: Local Centralized and Local Distributed Algorithms
We consider two models of computation: centralized local algorithms and local
distributed algorithms. Algorithms in one model are adapted to the other model
to obtain improved algorithms.
Distributed vertex coloring is employed to design improved centralized local
algorithms for: maximal independent set, maximal matching, and an approximation
scheme for maximum (weighted) matching over bounded degree graphs. The
improvement is threefold: the algorithms are deterministic, stateless, and the
number of probes grows polynomially in , where is the number of
vertices of the input graph.
The recursive centralized local improvement technique by Nguyen and
Onak~\cite{onak2008} is employed to obtain an improved distributed
approximation scheme for maximum (weighted) matching. The improvement is
twofold: we reduce the number of rounds from to for a
wide range of instances and, our algorithms are deterministic rather than
randomized
Towards Distributed Two-Stage Stochastic Optimization
The weighted vertex cover problem is concerned with selecting a subset of the vertices that covers a target set of edges with the objective of minimizing the total cost of the selected vertices. We consider a variant of this classic combinatorial optimization problem where the target edge set is not fully known; rather, it is characterized by a probability distribution. Adhering to the model of two-stage stochastic optimization, the execution is divided into two stages so that in the first stage, the decision maker selects some of the vertices based on the probabilistic forecast of the target edge set. Then, in the second stage, the edges in the target set are revealed and in order to cover them, the decision maker can augment the vertex subset selected in the first stage with additional vertices. However, in the second stage, the vertex cost increases by some inflation factor, so the second stage selection becomes more expensive.
The current paper studies the two-stage stochastic vertex cover problem in the realm of distributed graph algorithms, where the decision making process (in both stages) is distributed among the vertices of the graph. By combining the stochastic optimization toolbox with recent advances in distributed algorithms for weighted vertex cover, we develop an algorithm that runs in time O(log (?) / ?), sends O(m) messages in total, and guarantees to approximate the optimal solution within a (3 + ?)-ratio, where m is the number of edges in the graph, ? is its maximum degree, and 0 < ? < 1 is a performance parameter
An Order-based Algorithm for Minimum Dominating Set with Application in Graph Mining
Dominating set is a set of vertices of a graph such that all other vertices
have a neighbour in the dominating set. We propose a new order-based randomised
local search (RLS) algorithm to solve minimum dominating set problem in
large graphs. Experimental evaluation is presented for multiple types of
problem instances. These instances include unit disk graphs, which represent a
model of wireless networks, random scale-free networks, as well as samples from
two social networks and real-world graphs studied in network science. Our
experiments indicate that RLS performs better than both a classical greedy
approximation algorithm and two metaheuristic algorithms based on ant colony
optimisation and local search. The order-based algorithm is able to find small
dominating sets for graphs with tens of thousands of vertices. In addition, we
propose a multi-start variant of RLS that is suitable for solving the
minimum weight dominating set problem. The application of RLS in graph
mining is also briefly demonstrated
Approximation Algorithms for Multi-Criteria Traveling Salesman Problems
In multi-criteria optimization problems, several objective functions have to
be optimized. Since the different objective functions are usually in conflict
with each other, one cannot consider only one particular solution as the
optimal solution. Instead, the aim is to compute a so-called Pareto curve of
solutions. Since Pareto curves cannot be computed efficiently in general, we
have to be content with approximations to them.
We design a deterministic polynomial-time algorithm for multi-criteria
g-metric STSP that computes (min{1 +g, 2g^2/(2g^2 -2g +1)} + eps)-approximate
Pareto curves for all 1/2<=g<=1. In particular, we obtain a
(2+eps)-approximation for multi-criteria metric STSP. We also present two
randomized approximation algorithms for multi-criteria g-metric STSP that
achieve approximation ratios of (2g^3 +2g^2)/(3g^2 -2g +1) + eps and (1 +g)/(1
+3g -4g^2) + eps, respectively.
Moreover, we present randomized approximation algorithms for multi-criteria
g-metric ATSP (ratio 1/2 + g^3/(1 -3g^2) + eps) for g < 1/sqrt(3)), STSP with
weights 1 and 2 (ratio 4/3) and ATSP with weights 1 and 2 (ratio 3/2). To do
this, we design randomized approximation schemes for multi-criteria cycle cover
and graph factor problems.Comment: To appear in Algorithmica. A preliminary version has been presented
at the 4th Workshop on Approximation and Online Algorithms (WAOA 2006
The Maximum Traveling Salesman Problem with Submodular Rewards
In this paper, we look at the problem of finding the tour of maximum reward
on an undirected graph where the reward is a submodular function, that has a
curvature of , of the edges in the tour. This problem is known to be
NP-hard. We analyze two simple algorithms for finding an approximate solution.
Both algorithms require oracle calls to the submodular function. The
approximation factors are shown to be and
, respectively; so the second
method has better bounds for low values of . We also look at how these
algorithms perform for a directed graph and investigate a method to consider
edge costs in addition to rewards. The problem has direct applications in
monitoring an environment using autonomous mobile sensors where the sensing
reward depends on the path taken. We provide simulation results to empirically
evaluate the performance of the algorithms.Comment: Extended version of ACC 2013 submission (including p-system greedy
bound with curvature
Pseudo-Separation for Assessment of Structural Vulnerability of a Network
Based upon the idea that network functionality is impaired if two nodes in a
network are sufficiently separated in terms of a given metric, we introduce two
combinatorial \emph{pseudocut} problems generalizing the classical min-cut and
multi-cut problems. We expect the pseudocut problems will find broad relevance
to the study of network reliability. We comprehensively analyze the
computational complexity of the pseudocut problems and provide three
approximation algorithms for these problems.
Motivated by applications in communication networks with strict
Quality-of-Service (QoS) requirements, we demonstrate the utility of the
pseudocut problems by proposing a targeted vulnerability assessment for the
structure of communication networks using QoS metrics; we perform experimental
evaluations of our proposed approximation algorithms in this context
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