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Algorithms
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Graph Algorithms
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Graph Algorithms

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Combinatorial Optimization, Graph, and Network Algorithms".

Deadline for manuscript submissions: closed (31 October 2012) | Viewed by 93889

Special Issue Editor

Dr. Jesper Jansson

E-Mail Website
Guest Editor
Department of Communications and Computer Engineering, Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan
Interests: graph algorithms; bioinformatics; computational complexity; data structures
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This special issue of Algorithms is devoted to the design and analysis of algorithms for solving combinatorial problems of a theoretical or practical nature involving graphs, with a focus on computational complexity. Because of their simplicity and generality, graphs have been used for a long time in many different areas of science and engineering, e.g., to describe how objects such as the atoms of a molecule are connected or to express various types of constraints such as precedence constraints in a complex manufacturing process. More recently, graphs have found new applications in emerging research fields like social network analysis, the design of robust computer network topologies, frequency allocation in wireless networks, and bioinformatics (i.e., to represent metabolic pathways, protein-protein interactions, evolutionary relationships, or other kinds of structured biological information). The amount of data in such applications can be enormous, and therefore, the resulting graphs may be huge, which motivates further development of fast and space-efficient algorithms in the near future for solving various (old and new) graph problems exactly or approximately. We hereby invite papers presenting original research on graph algorithms to this special issue and hope to receive many high-quality submissions.

Dr. Jesper Jansson
Guest Editor

Keywords

  • computational complexity
  • approximation algorithms
  • fixed-parameter tractability
  • compact data structures for graphs
  • pattern matching in graphs
  • graph coloring
  • graph partitioning
  • graph drawing
  • network flow
  • fast algorithms for special graph classes

Published Papers (10 papers)

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Editorial

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38 KiB  
Editorial
Special Issue on Graph Algorithms
by Jesper Jansson
Algorithms 2013, 6(3), 457-458; https://doi.org/10.3390/a6030457 - 12 Aug 2013
Cited by 1 | Viewed by 5403
Abstract
This special issue of Algorithms is devoted to the design and analysis of algorithms for solving combinatorial problems of a theoretical or practical nature involving graphs, with a focus on computational complexity. Full article
(This article belongs to the Special Issue Graph Algorithms)

Research

Jump to: Editorial

222 KiB  
Article
New Heuristics for Rooted Triplet Consistency
by Soheil Jahangiri Tazehkand, Seyed Naser Hashemi and Hadi Poormohammadi
Algorithms 2013, 6(3), 396-406; https://doi.org/10.3390/a6030396 - 11 Jul 2013
Cited by 7 | Viewed by 6058
Abstract
Rooted triplets are becoming one of the most important types of input for reconstructing rooted phylogenies. A rooted triplet is a phylogenetic tree on three leaves and shows the evolutionary relationship of the corresponding three species. In this paper, we investigate the problem [...] Read more.
Rooted triplets are becoming one of the most important types of input for reconstructing rooted phylogenies. A rooted triplet is a phylogenetic tree on three leaves and shows the evolutionary relationship of the corresponding three species. In this paper, we investigate the problem of inferring the maximum consensus evolutionary tree from a set of rooted triplets. This problem is known to be APX-hard. We present two new heuristic algorithms. For a given set of m triplets on n species, the FastTree algorithm runs in O(m + α(n)n2) time, where α(n) is the functional inverse of Ackermann’s function. This is faster than any other previously known algorithms, although the outcome is less satisfactory. The Best Pair Merge with Total Reconstruction (BPMTR) algorithm runs in O(mn3) time and, on average, performs better than any other previously known algorithms for this problem. Full article
(This article belongs to the Special Issue Graph Algorithms)
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200 KiB  
Article
A Polynomial-Time Algorithm for Computing the Maximum Common Connected Edge Subgraph of Outerplanar Graphs of Bounded Degree
by Tatsuya Akutsu and Takeyuki Tamura
Algorithms 2013, 6(1), 119-135; https://doi.org/10.3390/a6010119 - 18 Feb 2013
Cited by 15 | Viewed by 10635
Abstract
The maximum common connected edge subgraph problem is to find a connected graph with the maximum number of edges that is isomorphic to a subgraph of each of the two input graphs, where it has applications in pattern recognition and chemistry. This paper [...] Read more.
The maximum common connected edge subgraph problem is to find a connected graph with the maximum number of edges that is isomorphic to a subgraph of each of the two input graphs, where it has applications in pattern recognition and chemistry. This paper presents a dynamic programming algorithm for the problem when the two input graphs are outerplanar graphs of a bounded vertex degree, where it is known that the problem is NP-hard, even for outerplanar graphs of an unbounded degree. Although the algorithm repeatedly modifies input graphs, it is shown that the number of relevant subproblems is polynomially bounded, and thus, the algorithm works in polynomial time. Full article
(This article belongs to the Special Issue Graph Algorithms)
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450 KiB  
Article
Computing the Eccentricity Distribution of Large Graphs
by Frank W. Takes and Walter A. Kosters
Algorithms 2013, 6(1), 100-118; https://doi.org/10.3390/a6010100 - 18 Feb 2013
Cited by 43 | Viewed by 16680
Abstract
The eccentricity of a node in a graph is defined as the length of a longest shortest path starting at that node. The eccentricity distribution over all nodes is a relevant descriptive property of the graph, and its extreme values allow the derivation [...] Read more.
The eccentricity of a node in a graph is defined as the length of a longest shortest path starting at that node. The eccentricity distribution over all nodes is a relevant descriptive property of the graph, and its extreme values allow the derivation of measures such as the radius, diameter, center and periphery of the graph. This paper describes two new methods for computing the eccentricity distribution of large graphs such as social networks, web graphs, biological networks and routing networks.We first propose an exact algorithm based on eccentricity lower and upper bounds, which achieves significant speedups compared to the straightforward algorithm when computing both the extreme values of the distribution as well as the eccentricity distribution as a whole. The second algorithm that we describe is a hybrid strategy that combines the exact approach with an efficient sampling technique in order to obtain an even larger speedup on the computation of the entire eccentricity distribution. We perform an extensive set of experiments on a number of large graphs in order to measure and compare the performance of our algorithms, and demonstrate how we can efficiently compute the eccentricity distribution of various large real-world graphs. Full article
(This article belongs to the Special Issue Graph Algorithms)
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3056 KiB  
Article
Dubins Traveling Salesman Problem with Neighborhoods: A Graph-Based Approach
by Jason T. Isaacs and João P. Hespanha
Algorithms 2013, 6(1), 84-99; https://doi.org/10.3390/a6010084 - 04 Feb 2013
Cited by 45 | Viewed by 10162
Abstract
We study the problem of finding the minimum-length curvature constrained closed path through a set of regions in the plane. This problem is referred to as the Dubins Traveling Salesperson Problem with Neighborhoods (DTSPN). An algorithm is presented that uses sampling to cast [...] Read more.
We study the problem of finding the minimum-length curvature constrained closed path through a set of regions in the plane. This problem is referred to as the Dubins Traveling Salesperson Problem with Neighborhoods (DTSPN). An algorithm is presented that uses sampling to cast this infinite dimensional combinatorial optimization problem as a Generalized Traveling Salesperson Problem (GTSP) with intersecting node sets. The GTSP is then converted to an Asymmetric Traveling Salesperson Problem (ATSP) through a series of graph transformations, thus allowing the use of existing approximation algorithms. This algorithm is shown to perform no worse than the best existing DTSPN algorithm and is shown to perform significantly better when the regions overlap. We report on the application of this algorithm to route an Unmanned Aerial Vehicle (UAV) equipped with a radio to collect data from sparsely deployed ground sensors in a field demonstration of autonomous detection, localization, and verification of multiple acoustic events. Full article
(This article belongs to the Special Issue Graph Algorithms)
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193 KiB  
Article
Tractabilities and Intractabilities on Geometric Intersection Graphs
by Ryuhei Uehara
Algorithms 2013, 6(1), 60-83; https://doi.org/10.3390/a6010060 - 25 Jan 2013
Cited by 9 | Viewed by 7321
Abstract
A graph is said to be an intersection graph if there is a set of objects such that each vertex corresponds to an object and two vertices are adjacent if and only if the corresponding objects have a nonempty intersection. There are several [...] Read more.
A graph is said to be an intersection graph if there is a set of objects such that each vertex corresponds to an object and two vertices are adjacent if and only if the corresponding objects have a nonempty intersection. There are several natural graph classes that have geometric intersection representations. The geometric representations sometimes help to prove tractability/intractability of problems on graph classes. In this paper, we show some results proved by using geometric representations. Full article
(This article belongs to the Special Issue Graph Algorithms)
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150 KiB  
Article
Computational Study on a PTAS for Planar Dominating Set Problem
by Marjan Marzban and Qian-Ping Gu
Algorithms 2013, 6(1), 43-59; https://doi.org/10.3390/a6010043 - 21 Jan 2013
Cited by 4 | Viewed by 7708
Abstract
The dominating set problem is a core NP-hard problem in combinatorial optimization and graph theory, and has many important applications. Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time approximation scheme (PTAS) for a class of NP-hard problems [...] Read more.
The dominating set problem is a core NP-hard problem in combinatorial optimization and graph theory, and has many important applications. Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time approximation scheme (PTAS) for a class of NP-hard problems in planar graphs. It is mentioned that the framework can be applied to obtain an O(2ckn) time, c is a constant, (1+1/k)-approximation algorithm for the planar dominating set problem. We show that the approximation ratio achieved by the mentioned application of the framework is not bounded by any constant for the planar dominating set problem. We modify the application of the framework to give a PTAS for the planar dominating set problem. With k-outer planar graph decompositions, the modified PTAS has an approximation ratio (1 + 2/k). Using 2k-outer planar graph decompositions, the modified PTAS achieves the approximation ratio (1+1/k) in O(22ckn) time. We report a computational study on the modified PTAS. Our results show that the modified PTAS is practical. Full article
(This article belongs to the Special Issue Graph Algorithms)
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189 KiB  
Article
Maximum Disjoint Paths on Edge-Colored Graphs: Approximability and Tractability
by Paola Bonizzoni, Riccardo Dondi and Yuri Pirola
Algorithms 2013, 6(1), 1-11; https://doi.org/10.3390/a6010001 - 27 Dec 2012
Cited by 10 | Viewed by 6860
Abstract
The problem of finding the maximum number of vertex-disjoint uni-color paths in an edge-colored graph has been recently introduced in literature, motivated by applications in social network analysis. In this paper we investigate the approximation and parameterized complexity of the problem. First, we [...] Read more.
The problem of finding the maximum number of vertex-disjoint uni-color paths in an edge-colored graph has been recently introduced in literature, motivated by applications in social network analysis. In this paper we investigate the approximation and parameterized complexity of the problem. First, we show that, for any constant ε > 0, the problem is not approximable within factor c1-ε, where c is the number of colors, and that the corresponding decision problem is W[1]-hard when parametrized by the number of disjoint paths. Then, we present a fixed-parameter algorithm for the problem parameterized by the number and the length of the disjoint paths. Full article
(This article belongs to the Special Issue Graph Algorithms)
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154 KiB  
Article
Extracting Co-Occurrence Relations from ZDDs
by Takahisa Toda
Algorithms 2012, 5(4), 654-667; https://doi.org/10.3390/a5040654 - 13 Dec 2012
Cited by 2 | Viewed by 8254
Abstract
A zero-suppressed binary decision diagram (ZDD) is a graph representation suitable for handling sparse set families. Given a ZDD representing a set family, we present an efficient algorithm to discover a hidden structure, called a co-occurrence relation, on the ground set. This computation [...] Read more.
A zero-suppressed binary decision diagram (ZDD) is a graph representation suitable for handling sparse set families. Given a ZDD representing a set family, we present an efficient algorithm to discover a hidden structure, called a co-occurrence relation, on the ground set. This computation can be done in time complexity that is related not to the number of sets, but to some feature values of the ZDD. We furthermore introduce a conditional co-occurrence relation and present an extraction algorithm, which enables us to discover further structural information. Full article
(This article belongs to the Special Issue Graph Algorithms)
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1432 KiB  
Article
Exact Algorithms for Maximum Clique: A Computational Study
by Patrick Prosser
Algorithms 2012, 5(4), 545-587; https://doi.org/10.3390/a5040545 - 19 Nov 2012
Cited by 65 | Viewed by 13716
Abstract
We investigate a number of recently reported exact algorithms for the maximum clique problem. The program code is presented and analyzed to show how small changes in implementation can have a drastic effect on performance. The computational study demonstrates how problem features and [...] Read more.
We investigate a number of recently reported exact algorithms for the maximum clique problem. The program code is presented and analyzed to show how small changes in implementation can have a drastic effect on performance. The computational study demonstrates how problem features and hardware platforms influence algorithm behaviour. The effect of vertex ordering is investigated. One of the algorithms (MCS) is broken into its constituent parts and we discover that one of these parts frequently degrades performance. It is shown that the standard procedure used for rescaling published results (i.e., adjusting run times based on the calibration of a standard program over a set of benchmarks) is unsafe and can lead to incorrect conclusions being drawn from empirical data. Full article
(This article belongs to the Special Issue Graph Algorithms)
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