Many problems that are relevant to sensor networks such as active sensing and coverage planning have objectives that exhibit diminishing returns and specifically are submodular. When each agent selects an action local space of actions, sequential maximization techniques for submodular function maximization obtain solutions within half of optimal even though such problems are often NP-Hard. However, adapting methods for submodular function maximization to distributed computation on sensor networks is challenging as sequential execution of planning steps is time-consuming and inefficient. Further, prior works have found that planners suffer severely impaired worst-case performance whenever large numbers of agents plan in parallel. This work develops new tools for analysis of submodular maximization problems which we apply to design of randomized distributed planners that provide constant-factor suboptimality approaching that of standard sequential planners. These bounds apply when the objective satisfies a higher-order monotonicity condition and when cumulative interactions between agents are proportional to the optimal objective value. Problems including generalizations of sensor coverage satisfy these conditions when agents have spatially local sensing actions and limited sensor range. We present simulation results for two such cases.

Distributed Submodular Maximization on Partition Matroids for Planning on Large Sensor Networks

Let N = {1,..., n} be a finite set of players and KN the complete graph on the node set N "union" {0}. Assume that the edges of KN have nonnegative weights and associate with each coalition S "subset of" N of players as cost c(S) the weight of a minimal spanning tree on the node set S "union" {0}. Using transformation from EXACT COVER BY 3-SETS, we exhibit the following problem to be NP-complete. Given the vector x "element of" "real numbers" N with x(N) = c(N) decide whether there exists a coalition S such that x(S) > c(S).

On the Complexity of Testing Membership in the Core of min-Cost Spanning Tree Games

Influence Maximization (IM) is a popular social network mining mechanism that mines influential users for viral marketing in social networks. Most of the Influence Maximization techniques employ either the independent cascade (IC) or linear threshold (LT) model in the node activation process. In the IC model, all the active in-neighbors are given a single chance to activate a node with a particular probability whereas, in the LT model, a node is activated if the aggregated influence of all the activated in-neighbors is no less than a threshold value. Thus, the threshold plays a significant role in the LT-based influence maximization. In this paper, we comprehensively survey the different threshold values used in various IM models. Based on the survey, we observe that the current studies lack threshold estimation models. Therefore, we develop a system model and propose four threshold estimation models based on influence-weight and degree distribution. The empirical results show that our algorithms generate threshold values that resemble the thresholds used by most IM algorithms along with faster running time. Besides, the proposed models are scalable and applicable to any influence-weight estimation technique and offer narrower threshold ranges rather than the broad ranges used in many existing works.

Threshold estimation models for linear threshold-based influential user mining in social networks

Models used to characterise blockchain features. A systematic literature review and bibliometric analysis

Prevention method of block withholding attack based on miners’ mining behavior in blockchain

Most studies on influence maximization focus on one-shot propagation, i.e. the influence is propagated from seed users only once following a probabilistic diffusion model and users' activation are determined via single cascade. In reality it is often the case that a user needs to be cumulatively impacted by receiving enough pieces of information propagated to her before she makes the final purchase decision. In this paper we model such cumulative activation as the following process: first multiple pieces of information are propagated independently in the social network following the classical independent cascade model, then the user will be activated (and adopt the product) if the cumulative pieces of information she received reaches her cumulative activation threshold. Two optimization problems are investigated under this framework: seed minimization with cumulative activation (SM-CA), which asks how to select a seed set with minimum size such that the number of cumulatively active nodes reaches a given requirement $\eta$; influence maximization with cumulative activation (IM-CA), which asks how to choose a seed set with fixed budget to maximize the number of cumulatively active nodes. For SM-CA problem, we design a greedy algorithm that yields a bicriteria $O(\ln n)$-approximation when $\eta=n$, where $n$ is the number of nodes in the network. For both SM-CA problem with $\eta<n$ and IM-CA problem, we prove strong inapproximability results. Despite the hardness results, we propose two efficient heuristic algorithms for SM-CA and IM-CA respectively based on the reverse reachable set approach. Experimental results on different real-world social networks show that our algorithms significantly outperform baseline algorithms.

pdf/cumulative-activation-in-social-networks-kwmlh4atbp.pdf

Cumulative Activation in Social Networks

Kempe, Kleinberg and Tardos (KKT) proposed the following conjecture about the general threshold model in social networks: local monotonicity and submodularity imply global monotonicity and submodularity. That is, if the threshold function of every node is monotone and submodular, then the spread function $\sigma(S)$ is monotone and submodular, where $S$ is a seed set and the spread function $\sigma(S)$ denotes the expected number of active nodes at termination of a diffusion process starting from $S$. The correctness of this conjecture has been proved by Mossel and Roch. In this paper, we first provide the concept AD-k (Alternating Difference-$k$) as a generalization of monotonicity and submodularity. Specifically, a set function $f$ is called \adk if all the $\ell$-th order differences of $f$ on all inputs have sign $(-1)^{\ell+1}$ for every $\ell\leq k$. Note that AD-1 corresponds to monotonicity and AD-2 corresponds to monotonicity and submodularity. We propose a refined version of KKT's conjecture: in the general threshold model, local AD-k implies global AD-k. The original KKT conjecture corresponds to the case for AD-2, and the case for AD-1 is the trivial one of local monotonicity implying global monotonicity. By utilizing continuous extensions of set functions as well as social graph constructions, we prove the correctness of our conjecture when the social graph is a directed acyclic graph (DAG). Furthermore, we affirm our conjecture on general social graphs when $k=\infty$.

pdf/higher-order-monotonicity-and-submodularity-of-influence-in-ww5h1zbm5u.pdf

Higher order monotonicity and submodularity of influence in social networks: from local to global.

Cooperative games provide an appropriate framework for fair and stable profit distribution in multiagent systems. In this paper, we study the algorithmic issues on path cooperative games that arise from the situations where some commodity flows through a network. In these games, a coalition of edges or vertices is successful if they establish a path from the source to the sink in the network, and lose otherwise. Based on dual theory of linear programming and the relationship with flow games, we provide the characterizations on the CS-core, least-core and nucleolus of path cooperative games. Furthermore, we show that the least-core and nucleolus are polynomially solvable for path cooperative games defined on both directed and undirected network.

The Least-Core and Nucleolus of Path Cooperative Games

Cooperative games provide an appropriate framework for fair and stable profit distribution in multiagent systems. In this paper, we study the algorithmic issues on path cooperative games that arise from the situations where some commodity flows through a network. In these games, a coalition of edges or vertices is successful if it enables a path from the source to the sink in the network, and lose otherwise. Based on dual theory of linear programming and the relationship with flow games, we provide the characterizations on the CS-core, least-core and nucleolus of path cooperative games. Furthermore, we show that the least-core and nucleolus are polynomially solvable for path cooperative games defined on both directed and undirected network.

The Least-core and Nucleolus of Path Cooperative Games

Coreness represents solution concepts related to core in cooperative games, which captures the stability of players. Motivated by the scale effect in social networks, economics and other scenario, we study the coreness of cooperative game with truncated submodular profit functions. Specifically, the profit function $f(\cdot )$ is defined by a truncation of a submodular function $\sigma (\cdot )$: $f(\cdot )=\sigma (\cdot )$ if $\sigma (\cdot )\ge \eta $ and $f(\cdot )=0$ otherwise, where $\eta $ is a given threshold. In this paper, we study the core and three core-related concepts of truncated submodular profit cooperative game. We first prove that whether core is empty can be decided in polynomial time and an allocation in core also can be found in polynomial time when core is not empty. When core is empty, we show hardness results and approximation algorithms for computing other core-related concepts including relative least-core value, absolute least-core value and least average dissatisfaction value.

Coreness of Cooperative Games with Truncated Submodular Profit Functions

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