On the Approximability of External-Influence-Driven Problems

Domination problems in general can capture situations in which some entities have an effect on other entities (and sometimes on themselves). The usual goal is to select a minimum number of entities that can influence a target group of entities or to influence a maximum number of target entities with a certain number of available influencers. In this work, we focus on the distinction between \textit{internal} and \textit{external} domination in the respective maximization problem. In particular, a dominator can dominate its entire neighborhood in a graph, internally dominating itself, while those of its neighbors which are not dominators themselves are externally dominated. We study the problem of maximizing the external domination that a given number of dominators can yield and we present a 0.5307-approximation algorithm for this problem. Moreover, our methods provide a framework for approximating a number of problems that can be cast in terms of external domination. In particular, we observe that an interesting interpretation of the maximum coverage problem can capture a new problem in elections, in which we want to maximize the number of \textit{externally represented} voters. We study this problem in two different settings, namely Non-Secrecy and Rational-Candidate, and provide approximability analysis for two alternative approaches; our analysis reveals, among other contributions, that an earlier resource allocation algorithm is, in fact, a 0.462-approximation algorithm for maximum external domination in directed graphs

Blockchain, consensus, and cryptography in electronic voting

Motivated by the recent trends to conduct electronic elections using blockchain technologies, we review the vast literature on cryptographic voting and assess the status of the field. We analyze the security requirements for voting systems and describe the major ideas behind the most influential cryptographic protocols for electronic voting. We focus on the great importance of consensus in the elimination of trusted third parties. Finally, we examine whether recent blockchain innovations can satisfy the strict requirements set for the security of electronic voting

Approximation Schemes for Subset Sum Ratio Problems

We consider the Subset Sum Ratio Problem ($SSR$), in which given a set of integers the goal is to find two subsets such that the ratio of their sums is as close to~1 as possible, and introduce a family of variations that capture additional meaningful requirements. Our main contribution is a generic framework that yields fully polynomial time approximation schemes (FPTAS) for problems in this family that meet certain conditions. We use our framework to design explicit FPTASs for two such problems, namely Two-Set Subset-Sum Ratio and Factor-$r$ Subset-Sum Ratio, with running time $\mathcal{O}(n^4/\varepsilon)$, which coincides with the best known running time for the original $SSR$ problem [15]

Improved Methods for Extracting Frequent Itemsets from Interim-Support Trees

Mining association rules in relational databases is a significant computational task with lots of applications. A fundamental ingredient of this task is the discovery of sets of attributes (itemsets) whose frequency in the data exceeds some threshold value. In previous work [9] we have introduced an approach to this problem which begins by carrying out an efficient partial computation of the necessary totals, storing these interim results in a set-enumeration tree. This work demonstrated that making ∗ Aris Pagourtzis and Dora Souliou were partially supported for this research by “Pythagoras