On the inapproximability of maximum intersection problems

Shieh, Min-Zheng; Tsai, Shi-Chun; Yang, Ming-Chuan

doi:10.1016/j.ipl.2012.06.014

Cited by 13 publications

(9 citation statements)

References 16 publications

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“…We show that the IMER problem is hard. Our proof reduces from the MAXIMUM-SUBSET-INTERSECTION problem that does not admit any constantfactor approximation polynomial-time algorithm unless P= NP, as showed by Shieh, Tsai, and Yang (2012).…”

Section: Results With Edge Removalmentioning

confidence: 97%

Election Control in Social Networks via Edge Addition or Removal

Castiglioni

Ferraioli

Gatti

2020

AAAI

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We focus on the scenario in which messages pro and/or against one or multiple candidates are spread through a social network in order to affect the votes of the receivers. Several results are known in the literature when the manipulator can make seeding by buying influencers. In this paper, instead, we assume the set of influencers and their messages to be given, and we ask whether a manipulator (e.g., the platform) can alter the outcome of the election by adding or removing edges in the social network. We study a wide range of cases distinguishing for the number of candidates or for the kind of messages spread over the network. We provide a positive result, showing that, except for trivial cases, manipulation is not affordable, the optimization problem being hard even if the manipulator has an unlimited budget (i.e., he can add or remove as many edges as desired). Furthermore, we prove that our hardness results still hold in a reoptimization variant, where the manipulator already knows an optimal solution to the problem and needs to compute a new solution once a local modification occurs (e.g., in bandit scenarios where estimations related to random variables change over time).

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Section: Results With Edge Removalmentioning

confidence: 97%

Election Control in Social Networks via Edge Addition or Removal

Castiglioni

Ferraioli

Gatti

2020

AAAI

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“…It is well known that MSI is NP-hard, and is NP-hard to approximate it within a factor a 0.5n 1−2 + O(1 − 3 ) [22]. Given the equivalence between PROXI and MSI, the theorem follows.…”

Section: A Hardness Of Proximentioning

confidence: 92%

“…In this case, the problem reduces to finding exactly one explanation E, of length l such that σ(E) is maximized. Since σ(E) is defined as the intersection of sets M p for all p ∈ E, the problem is equivalent to Maximum l-Subset Intersection (MSI) Problem [25], [22]: Given a collection of sets S = {S 1 , S 2 , . .…”

Section: A Hardness Of Proximentioning

confidence: 99%

Validating Network Value of Influencers by Means of Explanations

Bevilacqua

Clare

Goyal

et al. 2013

2013 IEEE 13th International Conference on Data Mining

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Abstract-Recently, there has been significant interest in social influence analysis. One of the central problems in this area is the problem of identifying influencers, such that by convincing these users to perform a certain action (like buying a new product), a large number of other users get influenced to follow the action. The client of such an application is essentially a marketer who would target these influencers for marketing a given new product, say by providing free samples or discounts. It is natural that before committing resources for targeting an influencer the marketer would be interested in validating the influence (or network value) of influencers returned. This requires digging deeper into such analytical questions as: who are their followers, on what actions (or products) they are influential, etc. However, the current approaches to identifying influencers largely work as a black box in this respect. The goal of this paper is to open up the black box, address these questions and provide informative and crisp explanations for validating the network value of influencers.We formulate the problem of providing explanations (called PROXI) as a discrete optimization problem of feature selection. We show that PROXI is not only NP-hard to solve exactly, it is NP-hard to approximate within any reasonable factor. Nevertheless, we show interesting properties of the objective function and develop an intuitive greedy heuristic. We perform detailed experimental analysis on two real world datasetsTwitter and Flixster, and show that our approach is useful in generating concise and insightful explanations of the influence distribution of users and that our greedy algorithm is effective and efficient with respect to several baselines.

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“…Finding the maximum intersection between the set of blocks disclosed to any set of c peers is an NP-hard problem [38] , thus we devised a conservative yet efficient algorithm to evaluate dynamically the number of blocks that can still be shared with a peer. The algorithm is divided into two main functions: one to update the counter of blocks disclosed to a peer ( Algorithm 1 -Update Blocks Disclosed), and the other to determine the number of blocks that can still be disclosed to a peer ( Algorithm 2 -Blocks to Disclose Left).…”

Section: Disclosure Constraintmentioning

confidence: 99%

Mistrustful P2P: Deterministic privacy-preserving P2P file sharing model to hide user content interests in untrusted peer-to-peer networks

2017

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a b s t r a c t P2P networks endowed individuals with the means to easily and efficiently distribute digital media over the Internet, but user legal liability issues may be raised as they also facilitate the unauthorized distribution and reproduction of copyrighted material. Traditional P2P file sharing systems focus on performance and scalability, disregarding any privacy or legal issues that may arise from their use. Lacking alternatives, and unaware of the privacy issues that arise from relaying traffic of insecure applications, users have adopted anonymity systems for P2P file sharing.This work aims at hiding user content interests from malicious peers through plausible deniability. The Mistrustful P2P model is built on the concept of mistrusting all the entities participating in the P2P network, hence its name. It provides a deterministic and configurable privacy protection that relies on cover content downloads to hide user content interests, has no trust requirements, and introduces several mechanisms to prevent user legal liability and reduce network overhead while enabling timely content downloads.We extend previous work on the Mistrustful P2P model by discussing its legal and ethical framework, assessing its feasibility for more use cases, providing a security analysis, comparing it against a traditional P2P file sharing model, and further defining and improving its main mechanisms.

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On the inapproximability of maximum intersection problems

Cited by 13 publications

References 16 publications

Election Control in Social Networks via Edge Addition or Removal

Election Control in Social Networks via Edge Addition or Removal

Validating Network Value of Influencers by Means of Explanations

Mistrustful P2P: Deterministic privacy-preserving P2P file sharing model to hide user content interests in untrusted peer-to-peer networks

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