Selected Algorithmic Papers from the International Workshop on Combinatorial Algorithms 2024

This Special Issue is dedicated to a selection of papers from the 35th International Workshop on Combinatorial Algorithms (IWOCA 2024), held in July 2024, in Ischia, Italy, with Adele A. Rescigno and Ugo Vaccaro as Program Co-chairs.

IWOCA is devoted to the broad area of combinatorial algorithms. The topics include algorithms and data structures, algorithms on strings and graphs, algorithms for big data and network analytics, algorithmic game theory, approximation algorithms, combinatorial generation, enumeration and counting, combinatorial optimization, complexity theory, combinatorics of words, computational algebra and geometry, computational biology, cryptography and information security, distributed and parallel algorithms, foundations of cloud computing, graph algorithms for social network analysis, graph drawing and labeling, graph theory and combinatorics, mobile agent, new paradigms of computation, online algorithms, parameterized and exact algorithms, probabilistic and randomized algorithms, and scheduling.

A selected group of authors were invited to submit an extended version of the conference publication to this Special Issue. However, the Special Issue was also open to papers that were not presented at the conference if they fell within the scope of the Issue.

After a rigorous peer review process in accordance with the high standards of the journal, the following five papers were selected for publication in this Special Issue.

The paper “Enumerating Minimal Vertex Covers and Dominating Sets with Capacity and/or Connectivity Constraints”, by Yasuaki Kobayashi, Kazuhiro Kurita, Kevin Mann, Yasuko Matsui, and Hirotaka Ono, considers the minimal vertex cover and minimal dominating sets with capacity and/or connectivity constraint enumeration problems. The authors develop polynomial delay enumeration algorithms for these problems on bounded degree graphs. For the case of minimal connected vertex covers, their algorithms run in polynomial delay, even in the class of d-claw-free graphs. This result is extended for bounded degree graphs and outputs in quasi-polynomial time on general graphs. To complement these algorithmic results, they show that the minimal connected vertex cover, minimal connected dominating set, and minimal capacitated vertex cover enumeration problems in 2-degenerated bipartite graphs are at least as hard as enumerating minimal transversals in hypergraphs.

The paper “Broadcasting in Stars of Cliques and Path-Connected Cliques”, by Akash Ambashankar and Hovhannes A. Harutyunyan, examined the broadcasting problem in network topologies represented by specialized clique-based structures. The primary objective was to propose an efficient algorithm for determining the broadcast time of any node in an arbitrary star of cliques and to rigorously prove its optimality. Additionally, the authors considered the broadcasting problem in path-connected cliques. For this structure, they developed a computationally efficient algorithm that leverages clique sizes and adjacency to optimize broadcast strategies, with broader implications for understanding communication in block graphs.

The paper “Perfect Roman Domination: Aspects of Enumeration and Parameterization”, by Kevin Mann and Henning Fernau, presents two ways to translate perfect code into the framework of Roman Dominating Functions. It discusses Perfect Roman Dominating Functions and Unique Response Roman Dominating Functions. The authors considered the complexity of the underlying decision problems on special graph classes. They proved that for split graphs, Unique Response Roman Dominating is polynomial time-solvable, while Perfect Roman Dominating is NP-complete. Beyond this, the authors give polynomial time algorithms for Perfect Roman Domination on interval graphs and for both decision problems on co-bipartite graphs. However, both problems are NP-complete on chordal bipartite graphs. They also show that both problems are W[1]-complete if parameterized by solution size and FPT if parameterized by the dual parameter or by clique width.

The paper “Text Indexing for Faster Gapped Pattern Matching” by Md Helal Hossen, Daniel Gibney, and Sharma V. Thankachan, revisits the version of the Gapped String Indexing problem, where the goal is to preprocess a text T to enable the efficient reporting of all occurrences of a gapped pattern in T. This problem has significant applications in computational biology and text mining. The hardness result in this problem suggests that any index with polylogarithmic query time must occupy near quadratic space. In a recent study [STACS 2024], Bille et al. presented a sub-quadratic space index. In this paper, the authors show how to achieve a gap-sensitive query time depending on the number of occurrences of a given gap and using sub-quadratic space.

The paper “Hardness and Approximability of Dimension Reduction on the Probability Simplex”, by Roberto Bruno, considers the following dimensionality reduction instance: Given an n-dimensional probability distribution p and an integer m < n, the aim is to find the m-dimensional probability distribution q that is the closest to p, using the Kullback–Leibler divergence as the measure of closeness. In general, dimension reduction is a technique used to transform data from a high-dimensional space into a lower-dimensional space, aiming to retain as much of the original information as possible. This approach is crucial in many disciplines like engineering, biology, astronomy, and economics. The author of this paper proves that the considered problem is strongly NP-hard and presents an approximation algorithm for it.

We would like to thank the authors for contributing to this Special Issue and the referees for their attentive and helpful work in the reviewing process.