Partial set cover problem and set multi-cover problem are two generalizations of the set cover problem. In this paper, we consider the partial set multi-cover problem which is a combination of them: given an element set E, a collection of sets $$\mathcal S\subseteq 2^E$$, a total covering ratio q, each set $$S\in \mathcal S$$ is associated with a cost $$c_S$$, each element $$e\in E$$ is associated with a covering requirement $$r_e$$, the goal is to find a minimum cost sub-collection $${\mathcal {S}}'\subseteq {\mathcal {S}}$$ to fully cover at least q|E| elements, where element e is fully covered if it belongs to at least $$r_e$$ sets of $${\mathcal {S}}'$$. Denote by $$r_{\max }=\max \{r_e:e\in E\}$$ the maximum covering requirement. We present an $$(O (r_{\max }\log ^2n(1+\ln (\frac{1}{\varepsilon })+\frac{1-q}{\varepsilon q})),1-\varepsilon )$$-bicriteria approximation algorithm, that is, the output of our algorithm has cost $$O(r_{\max }\log ^2 n(1+\ln (\frac{1}{\varepsilon })+\frac{1-q}{\varepsilon q}))$$ times of the optimal value while the number of fully covered elements is at least $$(1-\varepsilon )q|E|$$.

One model for viral marketing is the positive influence. In this model, an inactive node is changed into active if and only if at least half of its neighbors are already in active state. The positive influence model can be viewed as a special case of a general threshold model, in which the threshold function at each node has value one if at least a certain fraction of neighbors are in active state, and value 0 otherwise. This function can be proved to be monotonically increasing and nonsubmodular for any predefined fraction. Therefore, given a seed set, the number of influenced nodes is not submodular with respect to the size of the seed set. This fact makes those optimization problems related with positive influence very hard, including the minimum partial positive influence seeding problem: Given a social network G = (V, E) and a number 0 <; p <; 1, find a minimum seed set S which can positively influence at least p|V| nodes. In this paper, we present an O ((log n) 2 H ([pn]))-approximation algorithm for the minimum partial positive influence seeding problem, where n is the number of nodes, and H(·) is the Harmonic number.

Energy efficiency is an important issue in the study of wireless sensor networks. Given a set of targets and a set of sensors with bounded lifetime, the maximum lifetime k-coverage problem is to schedule active/sleeping status of sensors to maximize the time period during which every target is covered by at least k active sensors. Previously, it was known that when the sensing ranges are uniform, this problem has a polynomial time (4+ε)-approximation for k = 1 and (6+ε)-approximation for k = 2. In this paper, we make significant progress by showing that for any positive integer k, there exists a polynomial-time (3 + ε)-approximation.

In this paper, we consider the connected \(k\)-Center (\(CkC\)) problem, which can be seen as the classic \(k\)-Center problem with the constraint of internal connectedness, i.e., two nodes in a cluster are required to be connected by an internal path in the same cluster. \(CkC\) was first introduced by Ge et al. (ACM Trans Knowl Discov Data 2:7, 2008), in which they showed the \(NP\)-completeness for this problem and claimed a polynomial time approximation algorithm for it. However, the running time of their algorithm might not be polynomial, as one key step of their algorithm involves the computation of an \(NP\)-hard problem. We first present a simple polynomial time greedy-based \(2\)-approximation algorithm for the relaxation of \(CkC\)—the \(CkC^*\). Further, we give a \(6\)-approximation algorithm for \(CkC\).

Energy efficiency is an important issue in the study of wireless sensor networks. Given a homogeneous set of sensors with unit lifetime and a set of target points, find an active/sleeping schedule for sensors to maximize the lifetime of k-coverage, i.e., the time period during which every target point is covered by at least k active sensors. This is a well known problem in wireless sensor networks concerning with energy efficiency. When k = 1, it is called the maximum lifetime coverage problem which has been proved to have a polynomial-time (4 + ε)-approximation. When k ≥ 2, it is the maximum lifetime fault-tolerant coverage problem. Previous to this work, only in the case k = 2, a polynomial-time (6 + ε)-approximation is found. In this paper, we will make a significant progress by showing that for any positive integer k, there exists a polynomial-time (4 + ε)-approximation, and for k = 1,2, the performance ratio can be improved to (3 + ε).

Many routing protocols aim to improve delivery ratio, as well as reduce end-to-end delay time and total replicas in delay tolerant networks, or disruption tolerant network DTN. Most prior literatures study mobile ad hoc wireless networks without considering existing physical infrastructure. By taking them into considerations, we propose a routing protocol in DTNs considering consecutive forwarding quality CFQ, and conduct extensive simulations with real trace data, so as to evaluate the performance of CFQ. Simulation results show that CFQ outperforms most existing pure probability based forwarding protocols and most existing pure centrality-community based forwarding protocols in that its delay time and replicas are significantly reduced and its delivery ratio is significantly increased. At last, we are able to conclude that CFQ is more buffer-efficient and time-efficient.

One type of distributed systems is the client/server system consist of clients and servers. In order to improve the performance of such a system, client assignment strategy plays an important role. There are two criteria to evaluate the load on the servers - total load and load balance. The total load increases when the load balance decreases, vice versa. It has been proved that finding the best client assignment is NP-hard. In this paper, we propose a new model for the client assignment problem and design an algorithm based on Semidefinite programming (SDP). Our method has a (relaxed) performance ratio 0.87 when only 2 servers exist. In general case, our method becomes a heuristic, and the ratio of each iteration is 0.87. We are the first one to give these bounds. Our simulation results are compared with the state-of-art client assignment method, and our strategy outperforms it in terms of running time while keeps the load in similar level.

In this article dedicated to Professor Yue Minyi on the occasion of his 95th birthday, we present a new polynomial-time approximation scheme for the well-known Maximum Lifetime Coverage problem in wireless sensor networks. For any , this scheme contains an approximation algorithm with performance , which improves the performance ratio of previously known approximation in the literature.

Social networks have shown increasing popularity in real-world applications. Community detection is one of the fundamental problems. In this paper, we study how to partition the social networks into communities from a novel perspective. We define the mutual closeness and strangeness between each vertex pairs, and formulate our problem as a semidefinite program considering both the tightness of the same community and the looseness across different communities. Two NP-hard issues are addressed. One is to partition the social networks into communities through maximizing the tightness within the same community and the looseness between different communities. In the other issue, we take community volume into consideration such that the obtained communities have similar sizes. We give the mathematical models and the objective functions, and then analyze the performance bounds of the proposed algorithms. At last, we validate our method's effectiveness by comparing them with a highly effective existing partitioning method on real-world and artificial data sets.

When a large amount of sensors are randomly deployed into a field, how can we make a sleep/activate schedule for sensors to maximize the lifetime of target coverage in the field? This is a well-known problem, called Maximum Lifetime Coverage Problem (MLCP), which has been studied extensively in the literature. It is a long-standing open problem whether MLCP has a polynomial-time constant-approximation. The best-known approximation algorithm has performance ratio 1 + ln n where n is the number of sensors in the network, which was given by Berman et. al [1]. In their work, MLCP is reduced to Minimum Weight Sensor Coverage Problem (MWSCP) which is to find the minimum total weight of sensors to cover a given area or a given set of targets with a given set of weighted sensors. In this paper, we present a polynomial-time (4 + ∈)-approximation algorithm for MWSCP and hence we obtain a polynomial-time (4 + ξ)-approximation algorithm for MLCP, where ∈ >; 0, ξ >; 0.

It is well-known that the application of directional antennas can help conserve bandwidth and energy consumption in wireless networks. Thus, to achieve efficiency in wireless networks, we study a special virtual backbone (VB) using directional antennas, requiring that from one node to any other node in the network, there exists at least one directional shortest path all of whose intermediate directions should belong to the VB, named as Minimum rOuting Cost Directional VB (MOC-DVB). In addition, VB has been well studied in Unit Disk Graph (UDG). However, radio wave based communications in wireless networks may be interrupted by obstacles (e.g., buildings and mountains). Thus, in this paper, we model a network as a general directed graph. We prove that construction of a minimum MOC-DVB is an NP-hard problem in a general directed graph and in term of the size of MOC-DVB, there exists an unreachable lower bound of the polynomial-time selected MOC-DVB. Therefore, we propose a distributed approximation algorithm for constructing MOC-DVB with approximation ratio of 1 + ln K + 2ln δD, where K is the number of antennas on each node and δD is the maximum direction degree in the network. Extensive simulations demonstrate that our constructed MOC-DVB is much more efficient in the sense of MOC-DVB size and routing cost compared to other VBs.

It is well-known that the application of directional antennas can help conserve bandwidth and energy consumption in wireless networks. Thus, to achieve efficiency in wireless networks, we study a special virtual backbone (VB) using directional antennas, requiring that from one node to any other node in the network, there exists at least one directional shortest path all of whose intermediate directions should belong to the VB, named as Minimum rOuting Cost Directional VB (MOC-DVB). In addition, VB has been well studied in Unit Disk Graph (UDG). However, radio wave based communications in wireless networks may be interrupted by obstacles (e.g., buildings and mountains). Thus, in this paper, we model a network as a general directed graph. We prove that construction of a minimum MOC-DVB is an NP-hard problem in a general directed graph and in term of the size of MOC-DVB, there exists an unreachable lower bound of the polynomial-time selected MOC-DVB. Therefore, we propose a distributed approximation algorithm for constructing MOC-DVB with approximation ratio of 1 + lnK + 2lnδD, where K is the number of antennas on each node and δD is the maximum direction degree in the network. Extensive simulations demonstrate that our constructed MOC-DVB is much more efficient in the sense of MOC-DVB size and routing cost compared to other VBs.

Wireless networks can have properties not present in traditional wired networks. There is no physical backbone, and wireless nodes may be operating with a limited energy supply, as is the case for wireless sensor networks. We can adapt the idea of a wired network's physical backbone, creating virtual backbones. Therefore, in this dissertation, we examine how we might construct a virtual backbone for improved energy efficiency in broadcasting and routing. In detail, we consider cluster-based routing and CDS construction with guaranteed routing cost. We propose a new problem based on customer fairness, which looks for a minimum CDS in a given communication model with shortest path constraints. It guarantees that any two clients can communicate with each other through this CDS with hop counts the same as the best path from the original graph, which means that routing on such a CDS will not bring additional traffic for every client.Since the shortest path constraint is very strict, we study a CDS with relaxed constraint, in which we guarantee any two clients can communicate with hop count a most a constant factor from that in the original graph. We propose a heuristic algorithm, and we demonstrate that this relaxation is helpful since the CDS size is reduced greatly. To further save energy consumption, we apply directional antennas to CDS construction. We study a special virtual backbone (VB) using directional antennas, requiring that from one node to any other node in the network, there exists at least one directional shortest path all of whose intermediate directions should belong to the VB. Previously, Minimum Average Routing Path Clustering Problem (MARPCP) in multi-hop USNs was studied. The goal of this problem is to find a clustering of a USN so that the average clustering-based routing path from a node to it nearest underwater sink is minimized. We relaxed MARPCP to a special case of Minimum Weight Dominating Set Problem (MWDSP), for which we propose a PTAS. Derived from this result, we give a (3 + &epsi;)-approximation algorithm for MARPCP.

Topology control is one vital factor to a wireless network's efficiency. A Connected Dominating Set (CDS) can be a useful basis of a backbone topology construction. In this paper, a special CDS, named \alpha Minimum rOuting Cost CDS (\alpha-MOC-CDS), will be studied to improve the performance of CDS based broadcasting and routing. In this paper, we prove that construction of a minimum \alpha-MOC-CDS is NP-hard in a general graph and we propose a heuristic algorithm for construction of \alpha-MOC-CDS.

Social networks are attracting more attention from both industry and academia. Prior works on social networks focus on analyzing their roles in information propagation and decision making. However, few of these works consider the latency of information propagation, which is an essential issue especially in time-critical scenarios in social networks. In this paper, we introduce a new problem called FAST INFORMATION PROPAGATION PROBLEM, which is an optimization problem to identify the minimum set of influential nodes that could influence the whole network within a given latency bound d. We show our complexity result on this problem in the deterministic threshold models and present a greedy hill-climbing algorithm as the solution. For the d = 1 case, we prove that under the majority threshold model, this approximation algorithm has a performance ratio of H(Δ + 1) - 1 + ⌈ Δ/2⌉. Extensive experiments are conducted on a large collaboration network and the results show that our approximation algorithm outperforms the node-selection heuristics, which utilize the well-known approaches based on the node centrality in the social network analysis.

A Connected Dominating Set (CDS) can be used to construct a virtual backbone for wireless and mobile ad-hoc networks to make the system hierarchical and efficient. A virtual backbone can significantly improve network throughput, optimize broadband utilization, extend network lifetime, and reduce interference as well as packet retransmissions. Calculating a minimum backbone for a network is critical to reduce routing computation and energy consumption. This problem is a well-known NP-hard optimization problem, which has various applications in practice. In this paper, we propose a new problem based on customer fairness, which looks for a minimum CDS in a given communication model with shortest path constraints. It guarantees that any two clients can communicate with each other through this CDS with hop counts the same as the best path from the original graph, which means that routing on such a CDS will not bring additional traffic for every client. We name this problem as shortest path connected dominating set (SPCDS) and prove its NP-hardness by reduction from Hitting Set. Then we propose a centralized greedy algorithm and an efficient distributed approximation algorithm with approximation ratio Δ to solve SPCDS, where Δ is the maximum vertex degree in the given topology. We also analyze the time complexity, message complexity, and evaluate the efficiency of our distributed heuristic by several numerical experiments and comparisons with previous literatures.

In this paper we propose a new problem named energy-efficient multi-lingual cell broadcasting(EEML-CB) to support multi-lingual service in cell broadcasting system. We prove that the problem is NP-hard and then propose ILP model as well as a greedy algorithm named smart multi-lingual cell broadcasting (SMCB). We evaluated our heuristic by simulations.

Previously, we proposed Minimum Average Routing Path Clustering Problem (MARPCP) in multi-hop USNs. The goal of this problem is to find a clustering of a USN so that the average clustering-based routing path from a node to it nearest underwater sink is minimized. We relaxed MARPCP to a special case of Minimum Weight Dominating Set Problem (MWDSP), namely MWDSP-R. In addition, we showed the Performance Ratio (PR) of α-approximation algorithm for MWDSP-R is 3α for MARPCP. Based on this result, we showed the existence of a (15 + ∊)-approximation algorithm for MARPCP. In this paper, we first establish the NP-completeness of both MARPCP and MWDSP-R. Then, we propose a PTAS for MWDSP-R. By combining this result with our previous one, we have a (3 + ∊)-approximation algorithm for MARPCP.

Topology control is one of the major approaches to achieve energy efficiency as well as fault tolerance in wireless networks. In this paper, we study the dual power assignment problem for 2-edge connectivity and 2-vertex connectivity in the symmetric graphical model. The problem has arisen from the following practical origin. In a wireless ad hoc network where each node can switch its transmission power between high-level and low-level, how can we establish a fault-tolerant connected network topology in the most energy-efficient way? Specifically, the objective is to minimize the number of nodes assigned with high power and yet achieve 2-edge connectivity or 2-vertex connectivity. Note that to achieve a minimum number of high-power nodes is harder than an optimization problem in the same model whose objective is to minimize the total power cost. We first address these two optimization problems (2-edge connectivity and 2-vertex connectivity version) under the general graph model. Due to the NP-hardness, we propose an approximation algorithm, called prioritized edge selection algorithm, which achieves a 4-ratio approximation for 2-edge connectivity. After that, we modify the algorithm to solve the problem for 2-vertex connectivity and also achieve the same approximation ratio. We also show that the 4-ratio is tight for our algorithms in both cases.