A primal-dual algorithm for the minimum partial set multi-cover problem

Ran, Yingli; Shi, Yishuo; Tang, Changbing; Zhang, Zhao

doi:10.1007/s10878-019-00513-y

Cited by 16 publications

(5 citation statements)

References 23 publications

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“…Using the greedy algorithm, the nodes belonging to the same kind of community are connected by continuously merging with the community whose Q value grows the fastest or decreases the slowest [17]. Radicchi et al improved GN algorithm in 2003 and proposed a method to quantify the definition of community.…”

Section: Community Discovery Algorithm and Complex Networkmentioning

confidence: 99%

An Algorithm of Scene Information Collection in General Football Matches Based on Web Documents

Bin

Zhang

2021

Security and Communication Networks

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In order to obtain the scene information of the ordinary football game more comprehensively, an algorithm of collecting the scene information of the ordinary football game based on web documents is proposed. The commonly used T-graph web crawler model is used to collect the sample nodes of a specific topic in the football game scene information and then collect the edge document information of the football game scene information topic after the crawling stage of the web crawler. Using the feature item extraction algorithm of semantic analysis, according to the similarity of the feature items, the feature items of the football game scene information are extracted to form a web document. By constructing a complex network and introducing the local contribution and overlap coefficient of the community discovery feature selection algorithm, the features of the web document are selected to realize the collection of football game scene information. Experimental results show that the algorithm has high topic collection capabilities and low computational cost, the average accuracy of equilibrium is always around 98%, and it has strong quantification capabilities for web crawlers and communities.

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Section: Community Discovery Algorithm and Complex Networkmentioning

confidence: 99%

An Algorithm of Scene Information Collection in General Football Matches Based on Web Documents

Bin

Zhang

2021

Security and Communication Networks

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“…This is called a partial set multi-cover problem and is less studied than the previous one. Ran et al address the difficulty of the problem [14], while recent works [15], [16] provide heuristics with bounded error that still require solving an integer linear problem at each step, which is computationally impossible in our context.…”

Section: B Set Covering Algorithmsmentioning

confidence: 99%

“…where Φ is a matrix populated with the multiplicity of the coverage for each point. This is an extension of the set covering problem known as minimum partial set multi-cover problem, it is NPcomplete [16], and no efficient heuristics are yet known. To solve this problem, we start from a heuristic proposed for multi-camera visibility [20] and, after analyzing the specific problem and goal, we propose a simpler one with comparable performance.…”

Section: Maximizing W-coveragementioning

confidence: 99%

On Cost-Effective, Reliable Coverage for LoS Communications in Urban Areas

Gemmi

Cigno

Maccari

2022

IEEE Trans. Netw. Serv. Manage.

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The use of ultra high frequencies in 5G and future networks to improve transmission speeds and capacity requires that users' equipment remain in Line of Sight with the access antennas most of the service time. This requirement implies a change in perspective to plan the coverage: Antennas cannot be placed on roofs or remote antenna sites, and a robust coverage is based on multi-antenna visibility from any point. This paper tackles the problem of public street coverage in urban areas with a data-driven methodology. Starting from 3D digital maps, we formalize the problem of antenna placement as a set coverage problem and leverage powerful heuristics to implement a general algorithm that allows the exploration of different policies, returning the detailed coverage, the antenna placement, and the cost of the coverage. Results on 15 areas in 3 Italian cities show the properties of different policies and confirm for the first time on large scale real data the feasibility of Line of Sight communications with a sustainable number of antennas per km 2 .

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“…Ran et al were the first to study the MinPSMC problem [17]. It was shown that MinpU is a special case of the MinPSMC problem, and the MinPSMC problem is at least as hard as the DkS problem [16]. Because of this hardness result, Ran et al [15] began to study the MinPSMC problem in a geometric setting.…”

Section: Related Workmentioning

confidence: 99%

“…maximal consecutive segment covering p, point p is counted once. So, to prove (16), what we need to show is that there is only one maximal consecutive segment of Q covering p. For this purpose, we first prove the following claim.…”

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confidence: 99%

Approximation algorithm for minimum partial multi-cover under a geometric setting

et al. 2021

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In a minimum p union problem (MinpU), given a hypergraph G = (V, E) and an integer p, the goal is to find a set of p hyperedges E ′ ⊆ E such that the number of vertices covered by E ′ (that is | e∈E ′ e|) is minimized. It was known that MinpU is at least as hard as the densest k-subgraph problem. A question is: how about the problem in some geometric settings? In this paper, we consider the unit square MinpU problem (MinpU-US) in which V is a set of points on the plane, and each hyperedge of E consists of a set of points in a unit square. A ( 11+ε , 4)-bicriteria approximation algorithm is presented, that is, the algorithm finds at least p 1+ε unit squares covering at most 4opt points, where opt is the optimal value for the MinpU-US instance (the minimum number of points that can be covered by p unit squares).

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A primal-dual algorithm for the minimum partial set multi-cover problem

Cited by 16 publications

References 23 publications

An Algorithm of Scene Information Collection in General Football Matches Based on Web Documents

An Algorithm of Scene Information Collection in General Football Matches Based on Web Documents

On Cost-Effective, Reliable Coverage for LoS Communications in Urban Areas

Approximation algorithm for minimum partial multi-cover under a geometric setting

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