In this paper, we study the complexity of the periodic temporal graph realization problem with respect to upper bounds on the fastest path durations among its vertices. This constraint with respect to upper bounds appears naturally in transportation network design applications where, for example, a transportation network is given, and the goal is to appropriately schedule periodic travel routes, while not exceeding some desired upper bounds on the travel times. In our work, we focus only on underlying tree topologies, which are fundamental in many transportation network applications. As it turns out, the periodic upper-bounded temporal tree realization problem (TTR) has a very different computational complexity behavior than both (i) the classic graph realization problem with respect to shortest path distances in static graphs and (ii) the periodic temporal graph realization problem with exact given fastest travel times (which was recently introduced). First, we prove that, surprisingly, TTR is NP-hard, even for a constant period and when the input tree G satisfies at least one of the following conditions: (a) G is a star, or (b) G has constant maximum degree. Second, we prove that TTR is fixed-parameter tractable (FPT) with respect to the number of leaves in the input tree G, via a novel combination of techniques for totally unimodular matrices and mixed integer linear programming.

In the distributed localisation problem (DLP), n anonymous robots (agents) A(0),..., A(n-1) are located at arbitrary points p(0),..., p(n-1) is an element of S, where S is a Euclidean space. Initially, each agent A(i) operates within its own coordinate system in S, which may be inconsistent with those of other agents. The primary goal in DLP is for agents to reach a consensus on a unified (jointly agreed) coordinate system, in which all agents receive unique labels (coordinates) that accurately reflect the relative distances between all points p(0),..., p(n-1) in S. Extensive research on DLP has primarily focus on the feasibility and complexity of achieving consensus when agents have limited access to inter-agent distances, often due to missing or imprecise data. In contrast, this paper proposes a minimalist, computationally efficient distributed computing model where agents can query any pairwise relative positions, if needed. Specifically, we introduce a novel variant of population protocols, referred to as the spatial population protocols model. In this variant each agent can memorise one or a fixed number of coordinates, and when agents A(i) and A(j) interact, they can not only exchange their current knowledge but also either determine the distance d(ij) between them in S (distance query model) or obtain the vector (v(ij)) over right arrow spanning points p(i) and p(j) (vector query model). We propose and analyse several distributed localisation protocols, including: 1. Leader-based localisation protocol with distance queries We propose and analyse two leader-based localisation protocols that stabilise silently in o(n) time. These protocols leverage an efficient solution to the novel concept of multi-contact epidemic, a natural generalisation of the core communication tool in population protocols, known as the one-way epidemic. 2. Self-stabilising leader localisation protocol with distance queries We show how to effectively utilise a leader election mechanism within the leader-based localisation protocol to get a DLP protocol that self-stabilises silently in time O(n(log n/n)(1/(k+1)) log n) in k-dimensions. 3. Self-stabilising localisation protocol with vector queries We propose and analyse an optimally fast DLP protocol which self-stabilises silently in O(log n) time. 2012 ACM Subject Classification Theory of computation -> Distributed computing models

Through the lens of Tullock contests, we take a fresh look at the contest game for crowdsourcing reviews [11] as a Tullock contest game with discrete strategies: Each of n players, endowed with skills, strategically invests an effort for writing a review of some quality she chooses from a finite set [Q]; she is awarded a payment, out of a budget β , in proportion to her effort, and pays a player-specific cost, which is the product of effort and skill. So both the payment and the utility functions for a player are strictly concave in the player’s effort. Players are anonymous if skills are identical, and so is the game. We study the mixed Nash equilibria of the game, where no player could deviate to increase her expected utility; her support in a Nash equilibrium is the set of qualities she chooses with strictly positive probability. By strict concavity, mixed Nash equilibria have the Small Consecutive-Supports property: their supports have size at most 2. We show:

In a temporal network with discrete time-labels on its edges, entities and information can only "flow" along sequences of edges whose time-labels are non-decreasing (resp. increasing), i.e. along temporal (resp. strict temporal) paths. Nevertheless, in the model for temporal networks of [Kempe et al., JCSS, 2002], the individual time-labeled edges remain undirected: an edge $e=\{u,v\}$ with time-label $t$ specifies that "$u$ communicates with $v$ at time $t$". This is a symmetric relation between $u$ and $v$, and it can be interpreted that the information can flow in either direction. In this paper we make a first attempt to understand how the direction of information flow on one edge can impact the direction of information flow on other edges. More specifically, we introduce the notion of a temporal transitive orientation and we systematically investigate its algorithmic behavior in various situations. An orientation of a temporal graph is called temporally transitive if, whenever $u$ has a directed edge towards $v$ with time-label $t_1$ and $v$ has a directed edge towards $w$ with time-label $t_2\geq t_1$, then $u$ also has a directed edge towards $w$ with some time-label $t_3\geq t_2$. If we just demand that this implication holds whenever $t_2 > t_1$, the orientation is called strictly temporally transitive. Our main result is a conceptually simple, yet technically quite involved, polynomial-time algorithm for recognizing whether a given temporal graph $\mathcal{G}$ is transitively orientable. In wide contrast we prove that, surprisingly, it is NP-hard to recognize whether $\mathcal{G}$ is strictly transitively orientable. Additionally we introduce and investigate further related problems to temporal transitivity, notably among them the temporal transitive completion problem, for which we prove both algorithmic and hardness results.

In the distributed localization problem (DLP), n anonymous robots (agents) A(0), ... , A(n-1) begin at arbitrary positions p(0), ... , p(n-1) is an element of S, where S is a Euclidean space. Initially, each agent A(i) operates within its own coordinate system in S, which may be inconsistent with those of other agents. The primary goal in DLP is for agents to reach a consensus on a unified coordinate system that accurately reflects the relative positions of all points, p(0), ... , p(n-1), in S. Extensive research on DLP has primarily focused on the feasibility and complexity of achieving consensus when agents have limited access to inter-agent distances, often due to missing or imprecise data. In this paper, however, we examine a minimalist, computationally efficient model of distributed computing in which agents have access to all pairwise distances, if needed. Specifically, we introduce a novel variant of population protocols, referred to as the spatial population protocols model. In this variant each agent can memorise one or a fixed number of coordinates, and when agents A(i) and A(j) interact, they can not only exchange their current knowledge but also either determine the distance d(ij) between them in S (distance query model) or obtain the vector (vij) over right arrow spanning points p(i) and p(j) (vector query model). We present here a leader-based localisation protocol with distance queries.

Robots are becoming an increasingly common part of scientific work within laboratory environments. In this paper, we investigate the problem of designing schedules for completing a set of tasks at fixed locations with multiple robots in a laboratory. We represent the laboratory as a graph with tasks placed on fixed vertices and robots represented as agents, with the constraint that no two robots may occupy the same vertex, or traverse the same edge, at the same time. Each schedule is partitioned into a set of timesteps, corresponding to a walk through the graph (allowing for a robot to wait at a vertex to complete a task), with each timestep taking time equal to the time for a robot to move from one vertex to another and each task taking some given number of timesteps during the completion of which a robot must stay at the vertex containing the task. The goal is to determine a set of schedules, with one schedule for each robot, minimising the number of timesteps taken by the schedule taking the greatest number of timesteps within the set of schedules. We show that the problem of finding a task-fulfilling schedule in at most L timesteps is NP-complete for many simple classes of graphs. Explicitly, we provide this result for complete graphs, bipartite graphs, star graphs, and planar graphs. Finally, we provide positive results for line graphs, showing that we can find an optimal set of schedules for k robots completing m tasks of equal length of a path of length n in O(kmn) time, and a k-approximation when the length of the tasks is unbounded.

In this paper we consider the following total functional problem: Given a cubic Hamiltonian graph $G$ and a Hamiltonian cycle $C_0$ of $G$, how can we compute a second Hamiltonian cycle $C_1 \neq C_0$ of $G$? Cedric Smith proved in 1946, using a non-constructive parity argument, that such a second Hamiltonian cycle always exists. Our main result is an algorithm which computes the second Hamiltonian cycle in time $O(n \cdot 2^{(0.3-\varepsilon)n})$ time, for some positive constant $\varepsilon>0$, and in polynomial space, thus improving the state of the art running time for solving this problem. Our algorithm is based on a fundamental structural property of Thomason's lollipop algorithm, which we prove here for the first time. In the direction of approximating the length of a second cycle in a Hamiltonian graph $G$ with a given Hamiltonian cycle $C_0$ (where we may not have guarantees on the existence of a second Hamiltonian cycle), we provide a linear-time algorithm computing a second cycle with length at least $n - 4\alpha (\sqrt{n}+2\alpha)+8$, where $\alpha = \frac{\Delta-2}{\delta-2}$ and $\delta,\Delta$ are the minimum and the maximum degree of the graph, respectively. This approximation result also improves the state of the art.

We consider random simple temporal graphs in which every edge of the complete graph $K_n$ appears once within the time interval [0,1] independently and uniformly at random. Our main result is a sharp threshold on the size of any maximum $\delta$-clique (namely a clique with edges appearing at most $\delta$ apart within [0,1]) in random instances of this model, for any constant~$\delta$. In particular, using the probabilistic method, we prove that the size of a maximum $\delta$-clique is approximately $\frac{2\log{n}}{\log{\frac{1}{\delta}}}$ with high probability (whp). What seems surprising is that, even though the random simple temporal graph contains $\Theta(n^2)$ overlapping $\delta$-windows, which (when viewed separately) correspond to different random instances of the Erdos-Renyi random graphs model, the size of the maximum $\delta$-clique in the former model and the maximum clique size of the latter are approximately the same. Furthermore, we show that the minimum interval containing a $\delta$-clique is $\delta-o(\delta)$ whp. We use this result to show that any polynomial time algorithm for $\delta$-TEMPORAL CLIQUE is unlikely to have very large probability of success.

In this paper, we investigate the problem of designing schedules for completing a set of tasks at fixed locations with multiple robots in a laboratory. We represent the laboratory as a graph with tasks placed on fixed vertices and robots represented as agents, with the constraint that no two robots may occupy the same vertex at any given timestep. Each schedule is partitioned into a set of timesteps, corresponding to a walk through the graph (allowing for a robot to wait at a vertex to complete a task), with each timestep taking time equal to the time for a robot to move from one vertex to another and each task taking some given number of timesteps during the completion of which a robot must stay at the vertex containing the task. The goal is to determine a set of schedules, with one schedule for each robot, minimising the number of timesteps taken by the schedule taking the greatest number of timesteps within the set of schedules. We show that this problem is NP-complete for both star graphs (for k ≥ 2 robots), and planar graphs (for any number of robots). Finally, we provide positive results for path, cycle, and tadpole graphs, showing that we can find an optimal set of schedules for k robots completing m tasks of equal duration of a path of length n in O(kmn), O(k m n^2) time, and O(k^3 m^4 n) time respectively.

Crystalline materials enable essential technologies, and their properties are determined by their structures. Crystal structure prediction can thus play a central part in the design of new functional materials(1,2). Researchers have developed efficient heuristics to identify structural minima on the potential energy surface(3-5). Although these methods can often access all configurations in principle, there is no guarantee that the lowest energy structure has been found. Here we show that the structure of a crystalline material can be predicted with energy guarantees by an algorithm that finds all the unknown atomic positions within a unit cell by combining combinatorial and continuous optimization. We encode the combinatorial task of finding the lowest energy periodic allocation of all atoms on a lattice as a mathematical optimization problem of integer programming(6,7), enabling guaranteed identification of the global optimum using well-developed algorithms. A single subsequent local minimization of the resulting atom allocations then reaches the correct structures of key inorganic materials directly, proving their energetic optimality under clear assumptions. This formulation of crystal structure prediction establishes a connection to the theory of algorithms and provides the absolute energetic status of observed or predicted materials. It provides the ground truth for heuristic or data-driven structure prediction methods and is uniquely suitable for quantum annealers(8-10), opening a path to overcome the combinatorial explosion of atomic configurations.

Bayesian Decision Trees (DTs) are generally considered a more advanced and accurate model than a regular Decision Tree (DT) as they can handle complex and uncertain data. Existing work on Bayesian DTs uses Markov Chain Monte Carlo (MCMC) with an accept-reject mechanism and sample using naive proposals to proceed to the next iteration. This method can be slow because of the burn-in time needed. We can reduce the burn-in period by proposing a more sophisticated way of sampling or by designing a different numerical Bayesian approach. In this paper, we propose a replacement of the MCMC with an inherently parallel algorithm, the Sequential Monte Carlo (SMC), and a more effective sampling strategy inspired by the Evolutionary Algorithms (EA). Experiments show that SMC combined with the EA can produce more accurate results compared to MCMC in 100 times fewer iterations.

Graphs are fundamental tools for modelling relations among objects in various scientific fields. However, traditional static graphs have limitations when it comes to capturing the dynamic nature of real-world systems. To overcome this limitation, temporal graphs have been introduced as a framework to model graphs that change over time. In temporal graphs the edges among vertices appear and disappear at specific time steps, reflecting the temporal dynamics of the observed system, which allows us to analyse time dependent patterns and processes. In this paper we focus on the research related to sliding time windows in temporal graphs. Sliding time windows offer a way to analyse specific time intervals within the lifespan of a temporal graph. By sliding the window along the timeline, we can examine the graph’s characteristics and properties within different time periods. This paper provides an overview of the research on sliding time windows in temporal graphs. Although progress has been made in this field, there are still many interesting questions and challenges to be explored. We discuss some of the open problems and highlight their potential for future research. 2012 ACM Subject Classification Mathematics of computing → Graph theory; General and reference → Surveys and overviews

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC. Unfortunately, this can be slow, especially when considering large volumes of data. It is hard to parallelise the accept-reject component of the MCMC. None-the-less, we propose two methods for exploiting parallelism in the MCMC: in the first, we replace the MCMC with another numerical Bayesian approach, the Sequential Monte Carlo (SMC) sampler, which has the appealing property that it is an inherently parallel algorithm; in the second, we consider data partitioning. Both methods use multi-core processing with a HighPerformance Computing (HPC) resource. We test the two methods in various study settings to determine which method is the most beneficial for each test case. Experiments show that data partitioning has limited utility in the settings we consider and that the use of the SMC sampler can improve run-time (compared to the sequential implementation) by up to a factor of 343.

In a random intersection graph $$G_{n,m,p}$$ , each of n vertices selects a random subset of a set of m labels by including each label independently with probability p and edges are drawn between vertices that have at least one label in common. Among other applications, such graphs have been used to model social networks, in which individuals correspond to vertices and various features (e.g. ideas, interests) correspond to labels; individuals sharing at least one common feature are connected and this is abstracted by edges in random intersection graphs. In this paper, we consider the problem of finding maximum cliques when the input graph is $$G_{n,m,p}$$ . Current algorithms for this problem are successful with high probability only for relatively sparse instances, leaving the dense case mostly unexplored. We present a spectral algorithm for finding large cliques that processes vertices according to respective values in the second largest eigenvector of the adjacency matrix of induced subgraphs of the input graph corresponding to common neighbors of small cliques. Leveraging on the Single Label Clique Theorem from [16], we were able to construct random instances, without the need to externally plant a large clique in the input graph. In particular, we used label choices to determine the maximum clique and then concealed label information by just giving the adjacency matrix of $$G_{n, m, p}$$ as input to the algorithm. Our experimental evaluation showed that our spectral algorithm clearly outperforms existing polynomial time algorithms, both with respect to the failure probability and the approximation guarantee metrics, especially in the dense regime, thus suggesting that spectral properties of random intersection graphs may be also used to construct efficient algorithms for other NP-hard graph theoretical problems as well.

In this paper we investigate phenomena of spontaneous emergence or purposeful formation of highly organized structures in networks of related agents. We show that the formation of large organized structures requires exponentially large, in the size of the structures, networks. Our approach is based on Kolmogorov, or descriptional, complexity of networks viewed as finite size strings. We apply this approach to the study of the emergence or formation of simple organized, hierarchical, structures based on Sierpinski Graphs and we prove a Ramsey type theorem that bounds the number of vertices in Kolmogorov random graphs that contain Sierpinski Graphs as subgraphs. Moreover, we show that Sierpinski Graphs encompass close-knit relationships among their vertices that facilitate fast spread and learning of information when agents in their vertices are engaged in pairwise interactions modelled as two person games. Finally, we generalize our findings for any organized structure with succinct representations. Our work can be deployed, in particular, to study problems related to the security of networks by identifying conditions which enable or forbid the formation of sufficiently large insider subnetworks with malicious common goal to overtake the network or cause disruption of its operation.

In this paper we consider a variant of population protocols in which agents are allowed to be connected by edges, known as the constructors model. During an interaction between two agents the relevant connecting edge can be formed, maintained or eliminated by the transition function. The contributions of this paper are manifold. -- We propose and analyse a novel type of phase clocks allowing to count parallel time $\Theta(n\log n)$ in the constructors model. This new type of clocks can be also implemented in the standard population protocol model assuming a unique leader is available. -- The new clock enables an optimal $O(n\log n)$ parallel time spanning line construction which improves dramatically on the best previously known $O(n^2)$ parallel time solution. -- We define a probabilistic version of bubble-sort in which random comparisons are allowed only between adjacent numbers in the sequence being sorted. We show that rather surprisingly this probabilistic bubble-sort requires $O(n^2)$ comparisons in expectation, i.e., on the same level as its deterministic counterpart. -- We propose the first self-replication protocol allowing to reproduce a strand (line-segment carrying information) of length $k$ in parallel time $O(n(k+\log n)).$ This result is based on the probabilistic bubble-sort argument. This protocol permits also simultaneous replication where $l$ copies of the strand can be obtained in time $O(n(k+\log n)\log l).$ All protocols in this paper operate with high probability.

Decision Forests have attracted the academic community’s interest mainly due to their simplicity and transparency. This paper proposes two novel decision forest building techniques, called Maximal Information Coefficient Forest (MICF) and Pearson’s Correlation Coefficient Forest (PCCF). The proposed new algorithms use Pearson’s Correlation Coefficient (PCC) and Maximal Information Coefficient (MIC) as extra measures of the classification capacity score of each feature. Using those approaches, we improve the picking of the most convenient feature at each splitting node, the feature with the greatest Gain Ratio. We conduct experiments on 12 datasets that are available in the publicly accessible UCI machine learning repository. Our experimental results indicate that the proposed methods have the best average ensemble accuracy rank of 1.3 (for MICF) and 3.0 (for PCCF), compared to their closest competitor, Random Forest (RF), which has an average rank of 4.3. Additionally, the results from Friedman and Bonferroni-Dunn tests indicate statistically significant improvement.

In this paper, we study systems of distributed entities that can actively modify their communication network. This gives rise to distributed algorithms that apart from communication can also exploit network reconfiguration in order to carry out a given task. At the same time, the distributed task itself may now require global reconfiguration from a given initial network $G_s$ to a target network $G_f$ from a family of networks having some good properties, like small diameter. With reasonably powerful computational entities, there is a straightforward algorithm that transforms any $G_s$ into a spanning clique in $O(\log n)$ time. The algorithm can then compute any global function on inputs and reconfigure to any target network in one round. We argue that such a strategy is impractical for real applications. In real dynamic networks there is a cost associated with creating and maintaining connections. To formally capture such costs, we define three edge-complexity measures: the \emph{total edge activations}, the \emph{maximum activated edges per round}, and the \emph{maximum activated degree of a node}. The clique formation strategy highlighted above, maximizes all of them. We aim at improved algorithms that achieve (poly)log$(n)$ time while minimizing the edge-complexity for the general task of transforming any $G_s$ into a $G_f$ of diameter (poly)log$(n)$. We give three distributed algorithms. The first runs in $O(\log n)$ time, with at most $2n$ active edges per round, an optimal total of $O(n\log n)$ edge activations, a maximum degree $n-1$, and a target network of diameter 2. The second achieves bounded degree by paying an additional logarithmic factor in time and in total edge activations and gives a target network of diameter $O(\log n)$. Our third algorithm shows that if we slightly increase the maximum degree to polylog$(n)$ then we can achieve a running time of $o(\log^2 n)$.

Modern e-business policy aims to better frame and steer progress and advancements towards a legal and security aware framework. However, a large percentage of cases neglects the adoption of good security practices, exposing customers to potential risks. In this work, we present a hybrid approach upon self-assessment, self-improvement and self-regulation motivation, offered by the observAtory for Security and PrIvacy DAta (ASPIDA) system. To address privacy and security weaknesses we monitor and analyze a set of security and privacy metrics and indicators. The evaluation of the aforementioned criteria drives an outcome in the form of a digital badge of good practices for the specific website. This digital badge is a recognition and can be used by the e-business owners as an attraction that frames the services and content they offer to the public.