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Algorithms
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Approximation Algorithms for NP-Hard Problems
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Approximation Algorithms for NP-Hard Problems

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (31 December 2019) | Viewed by 10025

Special Issue Editors

Prof. Dr. Davide Bilò

E-Mail Website
Guest Editor
Department of Humanities and Social Sciences, University of Sassari, 07100 Sassari, Italy
Interests: algorithmic game theory; network creation games; Schelling games; fault-tolerant networks; graph spanners; distance oracles; approximation algorithms for np-hard problems
Special Issues, Collections and Topics in MDPI journals
Dr. Luciano Gualà

E-Mail Website
Guest Editor
Dipartimento di Ingegneria dell’ Impresa “Mario Lucertini”, Università di Roma “Tor Vergata”, Via del Politecnico 1, 00133 Roma, Italy
Interests: algorithmic game theory; fault tolerance; approximation algorithms for graph optimization problems; computational aspects of games and puzzles

Special Issue Information

Dear Colleagues,

With the rapid increase in computational power and due to the pervasiveness of algorithms in modern society, governments, institutions, universities, research centres, and scientists in general are getting more and more interested in finding algorithmic solutions to very sophisticated problems that are intractable most of the time.

The upcoming Special Issue “Approximation Algorithms for NP-Hard Problems” aims to provide a comprehensive view of the most recent advances in the design and development of approximate solutions for computationally difficult problems. We therefore invite you to submit high quality papers that focus on algorithmic and complexity theoretic aspects of NP-hard problems to this Special Issue. The topics include, but are not limited to:

  • approximation algorithms;
  • inapproximability results;
  • online algorithms and competitive analysis;
  • distributed and parallel approximation;
  • streaming algorithms;
  • combinatorial optimization in graphs and networks;
  • algorithmic game theory and mechanism design;
  • computational geometry problems.

Dr. Davide Bilò
Dr. Luciano Gualà
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (3 papers)

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15 pages, 353 KiB  
Article
Adding Edges for Maximizing Weighted Reachability
by Federico Corò, Gianlorenzo D'Angelo and Cristina M. Pinotti
Algorithms 2020, 13(3), 68; https://0-doi-org.brum.beds.ac.uk/10.3390/a13030068 - 18 Mar 2020
Cited by 3 | Viewed by 3254
Abstract
In this paper, we consider the problem of improving the reachability of a graph. We approach the problem from a graph augmentation perspective, in which a limited set size of edges is added to the graph to increase the overall number of reachable [...] Read more.
In this paper, we consider the problem of improving the reachability of a graph. We approach the problem from a graph augmentation perspective, in which a limited set size of edges is added to the graph to increase the overall number of reachable nodes. We call this new problem the Maximum Connectivity Improvement (MCI) problem. We first show that, for the purpose of solve solving MCI, we can focus on Directed Acyclic Graphs (DAG) only. We show that approximating the MCI problem on DAG to within any constant factor greater than 1 − 1 / e is NP -hard even if we restrict to graphs with a single source or a single sink, and the problem remains NP -complete if we further restrict to unitary weights. Finally, this paper presents a dynamic programming algorithm for the MCI problem on trees with a single source that produces optimal solutions in polynomial time. Then, we propose two polynomial-time greedy algorithms that guarantee ( 1 − 1 / e ) -approximation ratio on DAGs with a single source, a single sink or two sources. Full article
(This article belongs to the Special Issue Approximation Algorithms for NP-Hard Problems)
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17 pages, 343 KiB  
Article
Latency-Bounded Target Set Selection in Signed Networks
by Miriam Di Ianni and Giovanna Varricchio
Algorithms 2020, 13(2), 32; https://0-doi-org.brum.beds.ac.uk/10.3390/a13020032 - 29 Jan 2020
Cited by 3 | Viewed by 2863
Abstract
It is well-documented that social networks play a considerable role in information spreading. The dynamic processes governing the diffusion of information have been studied in many fields, including epidemiology, sociology, economics, and computer science. A widely studied problem in the area of viral [...] Read more.
It is well-documented that social networks play a considerable role in information spreading. The dynamic processes governing the diffusion of information have been studied in many fields, including epidemiology, sociology, economics, and computer science. A widely studied problem in the area of viral marketing is the target set selection: in order to market a new product, hoping it will be adopted by a large fraction of individuals in the network, which set of individuals should we “target” (for instance, by offering them free samples of the product)? In this paper, we introduce a diffusion model in which some of the neighbors of a node have a negative influence on that node, namely, they induce the node to reject the feature that is supposed to be spread. We study the target set selection problem within this model, first proving a strong inapproximability result holding also when the diffusion process is required to reach all the nodes in a couple of rounds. Then, we consider a set of restrictions under which the problem is approximable to some extent. Full article
(This article belongs to the Special Issue Approximation Algorithms for NP-Hard Problems)
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14 pages, 467 KiB  
Article
Constrained Connectivity in Bounded X-Width Multi-Interface Networks
by Alessandro Aloisio and Alfredo Navarra
Algorithms 2020, 13(2), 31; https://0-doi-org.brum.beds.ac.uk/10.3390/a13020031 - 26 Jan 2020
Cited by 4 | Viewed by 3105
Abstract
As technology advances and the spreading of wireless devices grows, the establishment of interconnection networks is becoming crucial. Main activities that involve most of the people concern retrieving and sharing information from everywhere. In heterogeneous networks, devices can communicate by means of multiple [...] Read more.
As technology advances and the spreading of wireless devices grows, the establishment of interconnection networks is becoming crucial. Main activities that involve most of the people concern retrieving and sharing information from everywhere. In heterogeneous networks, devices can communicate by means of multiple interfaces. The choice of the most suitable interfaces to activate (switch-on) at each device results in the establishment of different connections. A connection is established when at its endpoints the devices activate at least one common interface. Each interface is assumed to consume a specific percentage of energy for its activation. This is referred to as the cost of an interface. Due to energy consumption issues, and the fact that most of the devices are battery powered, special effort must be devoted to suitable solutions that prolong the network lifetime. In this paper, we consider the so-called p-Coverage problem where each device can activate at most p of its available interfaces in order to establish all the desired connections of a given network of devices. As the problem has been shown to be NP -hard even for p = 2 and unitary costs of the interfaces, algorithmic design activities have focused in particular topologies where the problem is optimally solvable. Following this trend, we first show that the problem is polynomially solvable for graphs (modeling the underlying network) of bounded treewidth by means of the Courcelle’s theorem. Then, we provide two optimal polynomial time algorithms to solve the problem in two subclasses of graphs with bounded treewidth that are graphs of bounded pathwidth and graphs of bounded carvingwidth. The two solutions are obtained by means of dynamic programming techniques. Full article
(This article belongs to the Special Issue Approximation Algorithms for NP-Hard Problems)
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