The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify the vulnerability of a graph to contagion. This paper introduces a simple farthest-first traversalbased approximation algorithm for this problem over general graphs. We refer to this proposal as the Burning Farthest-First (BFF) algorithm. BFF runs in O(n 3 ) steps and has a tight approximation factor of 3−2/b(G), where b(G) is the size of an optimal solution. The main attribute of BFF is that it has a better approximation factor than the state-of-the-art approximation algorithms for general graphs, which report an approximation factor of 3. Despite being simple, BFF proved practical when tested over some benchmark datasets.

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The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify how vulnerable a graph is to contagion. This paper introduces three mathematical formulations of the problem: an integer linear program (ILP) and two constraint satisfaction problems (CSP1 and CSP2). Thanks to off-the-shelf optimization software, these formulations can be solved optimally over arbitrary graphs; this is relevant because the only algorithms designed to date for this problem are approximation algorithms and heuristics, which do not guarantee to find optimal solutions. We empirically compared the proposed formulations using random graphs and off-the-shelf optimization software. The results show that CSP1 and CSP2 tend to reach optimal solutions in less time than the ILP. Therefore, we executed them over some benchmark graphs of order at most 5908. The previously best-known solutions for some of these graphs were improved. We draw some empirical observations from the experimental results. For instance, we find the tendency: the larger the graph’s optimal solution, the more difficult it is to find it. Finally, the resulting set of optimal solutions might be helpful as a benchmark dataset for the performance evaluation of non-exact algorithms.

In Outsourced Databases (ODB), Authenticated Query Processing (AQP) schemes offer to database owners the capabilities of verifying correctness, completeness, and/or freshness over query response, assuming untrusted providers. This paper focuses on the first two capabilities that are oriented to ensure integrity in structured data. The AQP solutions work at different level of granularity, mainly at tuple or cell; being the cell granularity the most recent approach that improves the precision of the query response. Another aspect of AQP solutions is the type of query that supports; selection, range, join, among others. Currently, only one solution works at cell level granularity and exclusively provides the correctness capability for selection queries. In this work, we propose a cryptographic scheme for authenticated query processing a cell level granularity that allows the data owner to verify the correctness and completeness of the selection and range query response. The scheme is based on a novel combination of cuckoo filters, bitmaps, and MACs. The cuckoo filter was used to achieve correctness and the bitmaps along with the MACS were used to ensure completeness. The performance of the scheme was evaluated using the Census-Income database. This data set contains weighted census data extracted from the 1994 and 1995 Current Population Surveys conducted by the U.S. Census Bureau. The experiments were carried out in two phases, the first phase consists of preparing the data. The second phase is the query process, where the queries are divided into select and range queries. The proposed scheme has the ability to provide correctness and completeness of a single cell without retrieving all the other attributes of the same row, minimizing network and storage costs. The scheme was designed and tested against attacks such as rows scrambling, columns scrambling, among others.

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A network paradigm called the Software-Defined Network (SDN) has recently been introduced. The idea of SDN is to separate the control logic from forwarding devices to enable a centralized control platform. However, SDN is still a distributed and asynchronous system: events can be triggered by any network entity, while messages and packets are prone to arbitrary and unpredictable transmission delays. Moreover, the absence of a global temporal reference results in a broad combinatorial range space of event order. During network updates, an out-of-order execution of events may result in a deviation from desirable consistent network update properties, leading, for example, to forwarding loops and forwarding black holes, among others. In this paper, we introduce a study of the Transient Forwarding Loop (TFL) phenomenon during SDN updates; for this, we define a formal model of the TFL based on causal dependencies that capture the conditions under which it may occur. Based on this model, we introduce an algorithm that ensures the causal dependencies of the system oriented toward TFL-free SDN updating. We formally prove that it is sufficient to ensure the causal dependencies in order to guarantee TFL-free network updates. Finally, we analytically evaluate our algorithm and discuss how it outperforms the state-of-the-art in terms of updating overhead. transmission delays) interface to establish networking. Furthermore, an out-of-order execution of events may occur since no global temporal reference is shared between network entities and message delays are arbitrary. This leads to the following problem: when updating a network while packet flows are taking routes to their destination, an out-of-order execution could give rise to non-deterministic behavior that temporarily deviates from network properties, which in turn may result in an inconsistent network update. Moreover and as a result, the network-wide view from the controller can transitorily be inconsistent with the current data plane state, which could affect the consistency of future network updates. To ensure consistent updates, depending on the network application, the network should align with some properties, such as no Transient Forwarding Loop (TFL) and no forwarding black hole, among others. The no TFL is one of the essential network properties desired by several network applications, including traffic engineering, virtual machine migration, and planned maintenance [4]. Informally, it ensures that a packet is never forwarded along a loop back during an arbitrary time interval to a forwarding device in the network where it was previously processed. To the best of our knowledge, (i) no study formally specifies under which conditions TFLs may occur in the context of SDNs. Furthermore, (ii) no solution to this problem aligns with the distributed and asynchronous nature of the SDNs. Indeed, the proposed solutions are centralized or synchronized. In fact, a centralized-based solution is associated with memory overhead: to perform updates, it makes use of the centr...

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