How Members of Covert Networks Conceal the Identities of Their Leaders

Centrality measures are the most commonly advocated social network analysis tools for identifying leaders of covert organizations. While the literature has predominantly focused on studying the effectiveness of existing centrality measures or developing new ones, we study the problem from the opposite perspective, by focusing on how a group of leaders can avoid being identified by centrality measures as key members of a covert network. More specifically, we analyze the problem of choosing a set of edges to be added to a network to decrease the leaders’ ranking according to three fundamental centrality measures, namely, degree, closeness, and betweenness. We prove that this problem is NP-complete for each measure. Moreover, we study how the leaders can construct a network from scratch, designed specifically to keep them hidden from centrality measures. We identify a network structure that not only guarantees to hide the leaders to a certain extent but also allows them to spread their influence across the network.

The (Coarse) Fine-Grained Structure of NP-Hard SAT and CSP Problems

We study the fine-grained complexity of NP-complete satisfiability (SAT) problems and constraint satisfaction problems (CSPs) in the context of the strong exponential-time hypothesis (SETH) , showing non-trivial lower and upper bounds on the running time. Here, by a non-trivial lower bound for a problem SAT (Γ) (respectively CSP (Γ)) with constraint language Γ, we mean a value c 0 > 1 such that the problem cannot be solved in time O ( c n ) for any c < c 0 unless SETH is false, while a non-trivial upper bound is simply an algorithm for the problem running in time O ( c n ) for some c < 2. Such lower bounds have proven extremely elusive, and except for cases where c 0 =2 effectively no such previous bound was known. We achieve this by employing an algebraic framework, studying constraint languages Γ in terms of their algebraic properties. We uncover a powerful algebraic framework where a mild restriction on the allowed constraints offers a concise algebraic characterization. On the relational side we restrict ourselves to Boolean languages closed under variable negation and partial assignment, called sign-symmetric languages. On the algebraic side this results in a description via partial operations arising from system of identities, with a close connection to operations resulting in tractable CSPs, such as near unanimity operations and edge operations . Using this connection we construct improved algorithms for several interesting classes of sign-symmetric languages, and prove explicit lower bounds under SETH. Thus, we find the first example of an NP-complete SAT problem with a non-trivial algorithm which also admits a non-trivial lower bound under SETH. This suggests a dichotomy conjecture with a close connection to the CSP dichotomy theorem: an NP-complete SAT problem admits an improved algorithm if and only if it admits a non-trivial partial invariant of the above form.

A Graph Theoretic Approach for Multi-Objective Budget Constrained Capsule Wardrobe Recommendation

Traditionally, capsule wardrobes are manually designed by expert fashionistas through their creativity and technical prowess. The goal is to curate minimal fashion items that can be assembled into several compatible and versatile outfits. It is usually a cost and time intensive process, and hence lacks scalability. Although there are a few approaches that attempt to automate the process, they tend to ignore the price of items or shopping budget. In this article, we formulate this task as a multi-objective budget constrained capsule wardrobe recommendation ( MOBCCWR ) problem. It is modeled as a bipartite graph having two disjoint vertex sets corresponding to top-wear and bottom-wear items, respectively. An edge represents compatibility between the corresponding item pairs. The objective is to find a 1-neighbor subset of fashion items as a capsule wardrobe that jointly maximize compatibility and versatility scores by considering corresponding user-specified preference weight coefficients and an overall shopping budget as a means of achieving personalization. We study the complexity class of MOBCCWR , show that it is NP-Complete, and propose a greedy algorithm for finding a near-optimal solution in real time. We also analyze the time complexity and approximation bound for our algorithm. Experimental results show the effectiveness of the proposed approach on both real and synthetic datasets.

Tries-Based Parallel Solutions for Generating Perfect Crosswords Grids

A general crossword grid generation is considered an NP-complete problem and theoretically it could be a good candidate to be used by cryptography algorithms. In this article, we propose a new algorithm for generating perfect crosswords grids (with no black boxes) that relies on using tries data structures, which are very important for reducing the time for finding the solutions, and offers good opportunity for parallelisation, too. The algorithm uses a special tries representation and it is very efficient, but through parallelisation the performance is improved to a level that allows the solution to be obtained extremely fast. The experiments were conducted using a dictionary of almost 700,000 words, and the solutions were obtained using the parallelised version with an execution time in the order of minutes. We demonstrate here that finding a perfect crossword grid could be solved faster than has been estimated before, if we use tries as supporting data structures together with parallelisation. Still, if the size of the dictionary is increased by a lot (e.g., considering a set of dictionaries for different languages—not only for one), or through a generalisation to a 3D space or multidimensional spaces, then the problem still could be investigated for a possible usage in cryptography.

k-Efficient domination: Algorithmic perspective

A set [Formula: see text] of a graph [Formula: see text] is called an efficient dominating set of [Formula: see text] if every vertex [Formula: see text] has exactly one neighbor in [Formula: see text], in other words, the vertex set [Formula: see text] is partitioned to some circles with radius one such that the vertices in [Formula: see text] are the centers of partitions. A generalization of this concept, introduced by Chellali et al. [k-Efficient partitions of graphs, Commun. Comb. Optim. 4 (2019) 109–122], is called [Formula: see text]-efficient dominating set that briefly partitions the vertices of graph with different radiuses. It leads to a partition set [Formula: see text] such that each [Formula: see text] consists a center vertex [Formula: see text] and all the vertices in distance [Formula: see text], where [Formula: see text]. In other words, there exist the dominators with various dominating powers. The problem of finding minimum set [Formula: see text] is called the minimum [Formula: see text]-efficient domination problem. Given a positive integer [Formula: see text] and a graph [Formula: see text], the [Formula: see text]-efficient Domination Decision problem is to decide whether [Formula: see text] has a [Formula: see text]-efficient dominating set of cardinality at most [Formula: see text]. The [Formula: see text]-efficient Domination Decision problem is known to be NP-complete even for bipartite graphs [M. Chellali, T. W. Haynes and S. Hedetniemi, k-Efficient partitions of graphs, Commun. Comb. Optim. 4 (2019) 109–122]. Clearly, every graph has a [Formula: see text]-efficient dominating set but it is not correct for efficient dominating set. In this paper, we study the following: [Formula: see text]-efficient domination problem set is NP-complete even in chordal graphs. A polynomial-time algorithm for [Formula: see text]-efficient domination in trees. [Formula: see text]-efficient domination on sparse graphs from the parametrized complexity perspective. In particular, we show that it is [Formula: see text]-hard on d-degenerate graphs while the original dominating set has Fixed Parameter Tractable (FPT) algorithm on d-degenerate graphs. [Formula: see text]-efficient domination on nowhere-dense graphs is FPT.

Proof Compression and NP Versus PSPACE II: Addendum

In [3] we proved the conjecture NP = PSPACE by advanced proof theoretic methods that combined Hudelmaier's cut-free sequent calculus for minimal logic (HSC) [5] with the horizontal compressing in the corresponding minimal Prawitz-style natural deduction (ND) [6]. In this Addendum we show how to prove a weaker result NP = coNP without referring to HSC. The underlying idea (due to the second author) is to omit full minimal logic and compress only \naive" normal tree-like ND refutations of the existence of Hamiltonian cycles in given non-Hamiltonian graphs, since the Hamiltonian graph problem in NP-complete. Thus, loosely speaking, the proof of NP = coNP can be obtained by HSC-elimination from our proof of NP = PSPACE [3].

Tackling the rich vehicle routing problem with nature-inspired algorithms

In the last decades, the classical Vehicle Routing Problem (VRP), i.e., assigning a set of orders to vehicles and planning their routes has been intensively researched. As only the assignment of order to vehicles and their routes is already an NP-complete problem, the application of these algorithms in practice often fails to take into account the constraints and restrictions that apply in real-world applications, the so called rich VRP (rVRP) and are limited to single aspects. In this work, we incorporate the main relevant real-world constraints and requirements. We propose a two-stage strategy and a Timeline algorithm for time windows and pause times, and apply a Genetic Algorithm (GA) and Ant Colony Optimization (ACO) individually to the problem to find optimal solutions. Our evaluation of eight different problem instances against four state-of-the-art algorithms shows that our approach handles all given constraints in a reasonable time.

Ranking Sets of Objects: The Complexity of Avoiding Impossibility Results

The problem of lifting a preference order on a set of objects to a preference order on a family of subsets of this set is a fundamental problem with a wide variety of applications in AI. The process is often guided by axioms postulating properties the lifted order should have. Well-known impossibility results by Kannai and Peleg and by Barbera and Pattanaik tell us that some desirable axioms – namely dominance and (strict) independence – are not jointly satisfiable for any linear order on the objects if all non-empty sets of objects are to be ordered. On the other hand, if not all non-empty sets of objects are to be ordered, the axioms are jointly satisfiable for all linear orders on the objects for some families of sets. Such families are very important for applications as they allow for the use of lifted orders, for example, in combinatorial voting. In this paper, we determine the computational complexity of recognizing such families. We show that it is \Pi_2^p-complete to decide for a given family of subsets whether dominance and independence or dominance and strict independence are jointly satisfiable for all linear orders on the objects if the lifted order needs to be total. Furthermore, we show that the problem remains coNP-complete if the lifted order can be incomplete. Additionally, we show that the complexity of these problems can increase exponentially if the family of sets is not given explicitly but via a succinct domain restriction. Finally, we show that it is NP-complete to decide for a family of subsets whether dominance and independence or dominance and strict independence are jointly satisfiable for at least one linear order on the objects.

Critical Nodes Detection in IoT-Based Cyber-Physical Systems

The new generation of fast, small, and energy-efficient devices that can connect to the internet are already used for different purposes in healthcare, smart homes, smart cities, industrial automation, and entertainment. One of the main requirements in all kinds of cyber-physical systems is a reliable communication platform. In a wired or wireless network, losing some special nodes may disconnect the communication paths between other nodes. Generally, these nodes, which are called critical nodes, have many undesired effects on the network. The authors focus on three different problems. The first problem is finding the nodes whose removal minimizes the pairwise connectivity in the residual network. The second problem is finding the nodes whose removal maximizes the number of connected components. Finally, the third problem is finding the nodes whose removal minimizes the size of the largest connected component. All three problems are NP-Complete, and the authors provide a brief survey about the existing approximated algorithms for these problems.

Polynomial time solution to NP-complete problem Hamiltonian cycle (P=NP Proof)

P vs NP is one of the open and most important mathematics/computer science questions that has not been answered since it was raised in 1971 despite its importance and a quest for a solution since 2000. P vs NP is a class of problems that no polynomial time algorithm exists for any. If any of the problems in the class gets solved in polynomial time, all can be solved as the problems are translatable to each other. One of the famous problems of this kind is Hamiltonian cycle. Here we propose a polynomial time algorithm with rigorous proof that it always finds a solution if there exists one. It is expected that this solution would address all problems in the class and have a major impact in diverse fields including computer science, engineering, biology, and cryptography.