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Algorithms
Special Issues
Graph Algorithms and Network Dynamics
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Graph Algorithms and Network Dynamics

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 (30 November 2020) | Viewed by 8010

Special Issue Editors

Dr. Stefano Leucci

E-Mail Website
Guest Editor
Department of Information Engineering, Computer Science and Mathematics, University ofL’Aquila, 67100 Coppito (AQ), Italy
Interests: exact and approximation algorithms on graphs; fault tolerant algorithms and data structures; algorithmic game theory
Dr. Marco Bressan

E-Mail Website
Guest Editor
Dipartimento di Informatica, University of Rome “La Sapienza”, 00198 Roma, Italy
Interests: large graph mining; randomized algorithms

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to the design and analysis of graph algorithms and network dynamics, with an emphasis on the interplay between the two. While graphs have proven to be a powerful tool to capture many fundamental problems, they have been traditionally considered from a static perspective. However, there is a deep and broad connection between graph algorithms and graph dynamics, with applications ranging from selfish optimization to distributed computing and the analysis of social and biological networks. On the one hand, the analysis of network dynamics provides precious insights for the design of efficient algorithms (e.g., information dissemination or community detection in large-scale social networks). On the other hand, algorithmic techniques for graph mining and analysis can give key information about the nature of the considered networks and on the mechanisms guiding their evolution (e.g., greedy routing and small-world graphs). We invite you to submit original contributions to this Special Issue on “Algorithms and Dynamics on Graphs”. Areas of interest include, but are not limited to the following:

  • Algorithmic aspects of networks;
  • Algorithmic game theory and mechanism design on graphs;
  • Models of graph and network evolution;
  • Algorithms for large-scale social networks;
  • Exact and approximation algorithms on graphs;
  • Probabilistic and randomized graph algorithms;
  • Parallel and distributed graph algorithms;
  • Stochastic graph processes.

Dr. Stefano Leucci
Dr. Marco Bressan
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.

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (3 papers)

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12 pages, 293 KiB  
Article
The Traffic Grooming Problem in Optical Networks with Respect to ADMs and OADMs: Complexity and Approximation
by Michele Flammini, Gianpiero Monaco, Luca Moscardelli, Mordechai Shalom and Shmuel Zaks
Algorithms 2021, 14(5), 151; https://doi.org/10.3390/a14050151 - 11 May 2021
Cited by 3 | Viewed by 2379
Abstract
All-optical networks transmit messages along lightpaths in which the signal is transmitted using the same wavelength in all the relevant links. We consider the problem of switching cost minimization in these networks. Specifically, the input to the problem under consideration is an optical [...] Read more.
All-optical networks transmit messages along lightpaths in which the signal is transmitted using the same wavelength in all the relevant links. We consider the problem of switching cost minimization in these networks. Specifically, the input to the problem under consideration is an optical network modeled by a graph G, a set of lightpaths modeled by paths on G, and an integer g termed the grooming factor. One has to assign a wavelength (modeled by a color) to every lightpath, so that every edge of the graph is used by at most g paths of the same color. A lightpath operating at some wavelength λ uses one Add/Drop multiplexer (ADM) at both endpoints and one Optical Add/Drop multiplexer (OADM) at every intermediate node, all operating at a wavelength of λ. Two lightpaths, both operating at the same wavelength λ, share the ADMs and OADMs in their common nodes. Therefore, the total switching cost due to the usage of ADMs and OADMs depends on the wavelength assignment. We consider networks of ring and path topology and a cost function that is a convex combination α·|OADMs|+(1−α)|ADMs| of the number of ADMs and the number of OADMs deployed in the network. We showed that the problem of minimizing this cost function is NP-complete for every convex combination, even in a path topology network with g=2. On the positive side, we present a polynomial-time approximation algorithm for the problem. Full article
(This article belongs to the Special Issue Graph Algorithms and Network Dynamics)
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28 pages, 399 KiB  
Article
Optimal Clustering in Stable Instances Using Combinations of Exact and Noisy Ordinal Queries
by Enrico Bianchi and Paolo Penna
Algorithms 2021, 14(2), 55; https://doi.org/10.3390/a14020055 - 8 Feb 2021
Cited by 2 | Viewed by 2480
Abstract
This work studies clustering algorithms which operates with ordinal or comparison-based queries (operations), a situation that arises in many active-learning applications where “dissimilarities” between data points are evaluated by humans. Typically, exact answers are costly (or difficult to obtain in large amounts) while [...] Read more.
This work studies clustering algorithms which operates with ordinal or comparison-based queries (operations), a situation that arises in many active-learning applications where “dissimilarities” between data points are evaluated by humans. Typically, exact answers are costly (or difficult to obtain in large amounts) while possibly erroneous answers have low cost. Motivated by these considerations, we study algorithms with non-trivial trade-offs between the number of exact (high-cost) operations and noisy (low-cost) operations with provable performance guarantees. Specifically, we study a class of polynomial-time graph-based clustering algorithms (termed Single-Linkage) which are widely used in practice and that guarantee exact solutions for stable instances in several clustering problems (these problems are NP-hard in the worst case). We provide several variants of these algorithms using ordinal operations and, in particular, non-trivial trade-offs between the number of high-cost and low-cost operations that are used. Our algorithms still guarantee exact solutions for stable instances of k-medoids clustering, and they use a rather small number of high-cost operations, without increasing the low-cost operations too much. Full article
(This article belongs to the Special Issue Graph Algorithms and Network Dynamics)
15 pages, 655 KiB  
Article
Hardness of an Asymmetric 2-Player Stackelberg Network Pricing Game
by Davide Bilò, Luciano Gualà and Guido Proietti
Algorithms 2021, 14(1), 8; https://doi.org/10.3390/a14010008 - 31 Dec 2020
Cited by 1 | Viewed by 2413
Abstract
Consider a communication network represented by a directed graph G=(V,E) of n nodes and m edges. Assume that edges in E are partitioned into two sets: a set C of edges with a fixed non-negative real cost, [...] Read more.
Consider a communication network represented by a directed graph G=(V,E) of n nodes and m edges. Assume that edges in E are partitioned into two sets: a set C of edges with a fixed non-negative real cost, and a set P of edges whose costs are instead priced by a leader. This is done with the final intent of maximizing a revenue that will be returned for their use by a follower, whose goal in turn is to select for his communication purposes a subnetwork of Gminimizing a given objective function of the edge costs. In this paper, we study the natural setting in which the follower computes a single-source shortest paths tree of G, and then returns to the leader a payment equal to the sum of the selected priceable edges. Thus, the problem can be modeled as a one-round two-player Stackelberg Network Pricing Game, but with the novelty that the objective functions of the two players are asymmetric, in that the revenue returned to the leader for any of her selected edges is not equal to the cost of such an edge in the follower’s solution. As is shown, for any ϵ>0 and unless P=NP, the leader’s problem of finding an optimal pricing is not approximable within n1/2−ϵ, while, if G is unweighted and the leader can only decide which of her edges enter in the solution, then the problem is not approximable within n1/3−ϵ. On the positive side, we devise a strongly polynomial-time O(n)-approximation algorithm, which favorably compares against the classic approach based on a single-price algorithm. Finally, motivated by practical applications, we consider the special cases in which edges in C are unweighted and happen to form two popular network topologies, namely stars and chains, and we provide a comprehensive characterization of their computational tractability. Full article
(This article belongs to the Special Issue Graph Algorithms and Network Dynamics)
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