64 research outputs found
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 (), 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- Subset-Sum Ratio, with running time , which coincides with the best known running time for the original problem [15]
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