Finding Disjoint Paths on Edge-Colored Graphs: More Tractability Results

The problem of finding the maximum number of vertex-disjoint uni-color paths in an edge-colored graph (called MaxCDP) has been recently introduced in literature, motivated by applications in social network analysis. In this paper we investigate how the complexity of the problem depends on graph parameters (namely the number of vertices to remove to make the graph a collection of disjoint paths and the size of the vertex cover of the graph), which makes sense since graphs in social networks are not random and have structure. The problem was known to be hard to approximate in polynomial time and not fixed-parameter tractable (FPT) for the natural parameter. Here, we show that it is still hard to approximate, even in FPT-time. Finally, we introduce a new variant of the problem, called MaxCDDP, whose goal is to find the maximum number of vertex-disjoint and color-disjoint uni-color paths. We extend some of the results of MaxCDP to this new variant, and we prove that unlike MaxCDP, MaxCDDP is already hard on graphs at distance two from disjoint paths.Comment: Journal version in JOC

The Longest Run Subsequence Problem: Further Complexity Results

Longest Run Subsequence is a problem introduced recently in the context of the scaffolding phase of genome assembly (Schrinner et al., WABI 2020). The problem asks for a maximum length subsequence of a given string that contains at most one run for each symbol (a run is a maximum substring of consecutive identical symbols). The problem has been shown to be NP-hard and to be fixed-parameter tractable when the parameter is the size of the alphabet on which the input string is defined. In this paper we further investigate the complexity of the problem and we show that it is fixed-parameter tractable when it is parameterized by the number of runs in a solution, a smaller parameter. Moreover, we investigate the kernelization complexity of Longest Run Subsequence and we prove that it does not admit a polynomial kernel when parameterized by the size of the alphabet or by the number of runs. Finally, we consider the restriction of Longest Run Subsequence when each symbol has at most two occurrences in the input string and we show that it is APX-hard

Correcting Gene Trees by Leaf Insertions: Complexity and Approximation

Abstract Gene tree correction has recently gained interest in phylogenomics, as it gives insights in understanding the evolution of gene families. Following some recent approaches based on leaf edit operations, we consider a variant of the problem where a gene tree is corrected by inserting leaves with labels in a multiset M. We show that the problem of deciding whether a gene tree can be corrected by inserting leaves with labels in M is NP-complete. Then, we consider an optimization variant of the problem that asks for the correction of a gene tree with leaves labeled by a multiset M ′ , with M ′ ⊇ M , having minimum size. For this optimization variant of the problem, we present a factor 2 approximation algorithm

Pure Parsimony Xor Haplotyping

The haplotype resolution from xor-genotype data has been recently formulated as a new model for genetic studies. The xor-genotype data is a cheaply obtainable type of data distinguishing heterozygous from homozygous sites without identifying the homozygous alleles. In this paper we propose a formulation based on a well-known model used in haplotype inference: pure parsimony. We exhibit exact solutions of the problem by providing polynomial time algorithms for some restricted cases and a fixed-parameter algorithm for the general case. These results are based on some interesting combinatorial properties of a graph representation of the solutions. Furthermore, we show that the problem has a polynomial time k-approximation, where k is the maximum number of xor-genotypes containing a given SNP. Finally, we propose a heuristic and produce an experimental analysis showing that it scales to real-world large instances taken from the HapMap project

Genetic algorithms for finding episodes in temporal networks

Castelli, M., Dondi, R., & Hosseinzadeh, M. M. (2020). Genetic algorithms for finding episodes in temporal networks. Procedia Computer Science, 176, 215-224. https://doi.org/10.1016/j.procs.2020.08.023The evolution of networks is a fundamental topic in network analysis and mining. One of the approaches that has been recently considered in this field is the analysis of temporal networks, where relations between elements can change over time. A relevant problem in the analysis of temporal networks is the identification of cohesive or dense subgraphs since they are related to communities. In this contribution, we present a method based on genetic algorithms and on a greedy heuristic to identify dense subgraphs in a temporal network. We present experimental results considering both synthetic and real-networks, and we analyze the performance of the proposed method when varying the size of the population and the number of generations. The experimental results show that our heuristic generally performs better in terms of quality of the solutions than the state-of-art method for this problem. On the other hand, the state-of-art method is faster, although comparable with our method, when the size of the population and the number of generations are limited to small values.publishersversionpublishe