MRF Optimization by Graph Approximation

Graph cuts-based algorithms have achieved great success in energy minimization for many computer vision applications. These algorithms provide approximated solutions for multi-label energy functions via move-making approach. This approach fuses the current solution with a proposal to generate a lower-energy solution. Thus, generating the appropriate proposals is necessary for the success of the move-making approach. However, not much research efforts has been done on the generation of "good" proposals, especially for non-metric energy functions. In this paper, we propose an application-independent and energy-based approach to generate "good" proposals. With these proposals, we present a graph cuts-based move-making algorithm called GA-fusion (fusion with graph approximation-based proposals). Extensive experiments support that our proposal generation is effective across different classes of energy functions. The proposed algorithm outperforms others both on real and synthetic problems.Comment: CVPR201

HEMI: Hyperedge Majority Influence Maximization

In this work, we consider the problem of influence maximization on a hypergraph. We first extend the Independent Cascade (IC) model to hypergraphs, and prove that the traditional influence maximization problem remains submodular. We then present a variant of the influence maximization problem (HEMI) where one seeks to maximize the number of hyperedges, a majority of whose nodes are influenced. We prove that HEMI is non-submodular under the diffusion model proposed.Comment: 10 pages, Accepted for oral presentation at the Social Influence Analysis (SocInf) Workshop, IJCAI 201

On Quadratization of Pseudo-Boolean Functions

We survey current term-wise techniques for quadratizing high-degree pseudo-Boolean functions and introduce a new one, which allows multiple splits of terms. We also introduce the first aggregative approach, which splits a collection of terms based on their common parts.Comment: 11 page

Boosting Information Spread: An Algorithmic Approach

The majority of influence maximization (IM) studies focus on targeting influential seeders to trigger substantial information spread in social networks. In this paper, we consider a new and complementary problem of how to further increase the influence spread of given seeders. Our study is motivated by the observation that direct incentives could "boost" users so that they are more likely to be influenced by friends. We study the $k$-boosting problem which aims to find $k$ users to boost so that the final "boosted" influence spread is maximized. The $k$-boosting problem is different from the IM problem because boosted users behave differently from seeders: boosted users are initially uninfluenced and we only increase their probability to be influenced. Our work also complements the IM studies because we focus on triggering larger influence spread on the basis of given seeders. Both the NP-hardness of the problem and the non-submodularity of the objective function pose challenges to the $k$-boosting problem. To tackle the problem on general graphs, we devise two efficient algorithms with the data-dependent approximation ratio. For the $k$-boosting problem on bidirected trees, we present an efficient greedy algorithm and a rounded dynamic programming that is a fully polynomial-time approximation scheme. We conduct extensive experiments using real social networks and synthetic bidirected trees. We show that boosting solutions returned by our algorithms achieves boosts of influence that are up to several times higher than those achieved by boosting solutions returned by intuitive baselines, which have no guarantee of solution quality. We also explore the "budget allocation" problem in our experiments. Compared with targeting seeders with all budget, larger influence spread is achieved when we allocation the budget to both seeders and boosted users

IoU is not submodular

This short article aims at demonstrate that the Intersection over Union (or Jaccard index) is not a submodular function. This mistake has been made in an article which is cited and used as a foundation in another article. The Intersection of Union is widely used in machine learning as a cost function especially for imbalance data and semantic segmentation

Joint Placement and Allocation of VNF Nodes with Budget and Capacity Constraints

With the advent of Network Function Virtualization (NFV), network services that traditionally run on proprietary dedicated hardware can now be realized using Virtual Network Functions (VNFs) that are hosted on general-purpose commodity hardware. This new network paradigm offers a great flexibility to Internet service providers (ISPs) for efficiently operating their networks (collecting network statistics, enforcing management policies, etc.). However, introducing NFV requires an investment to deploy VNFs at certain network nodes (called VNF-nodes), which has to account for practical constraints such as the deployment budget and the VNF-node capacity. To that end, it is important to design a joint VNF-nodes placement and capacity allocation algorithm that can maximize the total amount of network flows that are fully processed by the VNF-nodes while respecting such practical constraints. In contrast to most prior work that often neglects either the budget constraint or the capacity constraint, we explicitly consider both of them. We prove that accounting for these constraints introduces several new challenges. Specifically, we prove that the studied problem is not only NP-hard but also non-submodular. To address these challenges, we introduce a novel relaxation method such that the objective function of the relaxed placement subproblem becomes submodular. Leveraging this useful submodular property, we propose two algorithms that achieve an approximation ratio of $\frac{1}{2}(1-1/e)$ and $\frac{1}{3}(1-1/e)$ for the original non-relaxed problem, respectively. Finally, we corroborate the effectiveness of the proposed algorithms through extensive evaluations using trace-driven simulations

Seeding Influential Nodes in Non-Submodular Models of Information Diffusion

We consider the model of information diffusion in social networks from \cite{Hui2010a} which incorporates trust (weighted links) between actors, and allows actors to actively participate in the spreading process, specifically through the ability to query friends for additional information. This model captures how social agents transmit and act upon information more realistically as compared to the simpler threshold and cascade models. However, it is more difficult to analyze, in particular with respect to seeding strategies. We present efficient, scalable algorithms for determining good seed sets -- initial nodes to inject with the information. Our general approach is to reduce our model to a class of simpler models for which provably good sets can be constructed. By tuning this class of simpler models, we obtain a good seed set for the original more complex model. We call this the \emph{projected greedy approach} because you `project' your model onto a class of simpler models where a greedy seed set selection is near-optimal. We demonstrate the effectiveness of our seeding strategy on synthetic graphs as well as a realistic San Diego evacuation network constructed during the 2007 fires.Comment: corrections to contact inf

Strong Price of Anarchy and Coalitional Dynamics

We introduce a framework for studying the effect of cooperation on the quality of outcomes in utility games. Our framework is a coalitional analog of the smoothness framework of non-cooperative games. Coalitional smoothness implies bounds on the strong price of anarchy, the loss of quality of coalitionally stable outcomes, as well as bounds on coalitional versions of coarse correlated equilibria and sink equilibria, which we define as out-of-equilibrium myopic behavior as determined by a natural coalitional version of best-response dynamics. Our coalitional smoothness framework captures existing results bounding the strong price of anarchy of network design games. We show that in any monotone utility-maximization game, if each player's utility is at least his marginal contribution to the welfare, then the strong price of anarchy is at most 2. This captures a broad class of games, including games with a very high price of anarchy. Additionally, we show that in potential games the strong price of anarchy is close to the price of stability, the quality of the best Nash equilibrium

On Misinformation Containment in Online Social Networks

The widespread online misinformation could cause public panic and serious economic damages. The misinformation containment problem aims at limiting the spread of misinformation in online social networks by launching competing campaigns. Motivated by realistic scenarios, we present the first analysis of the misinformation containment problem for the case when an arbitrary number of cascades are allowed. This paper makes four contributions. First, we provide a formal model for multi-cascade diffusion and introduce an important concept called as cascade priority. Second, we show that the misinformation containment problem cannot be approximated within a factor of $\Omega(2^{\log^{1-\epsilon}n^4})$ in polynomial time unless NP \subseteq DTIME(n^{\polylog{n}}). Third, we introduce several types of cascade priority that are frequently seen in real social networks. Finally, we design novel algorithms for solving the misinformation containment problem. The effectiveness of the proposed algorithm is supported by encouraging experimental results.Comment: NIPS 201

Input Matrix Construction and Approximation Using a Graphic Approach

Given a state transition matrix (STM), we reinvestigate the problem of constructing the sparest input matrix with a fixed number of inputs to guarantee controllability. We give a new and simple graph theoretic characterization for the sparsity pattern of input matrices to guarantee controllability for a general STM admitting multiple eigenvalues, and provide a deterministic procedure with polynomial time complexity to construct real valued input matrices with arbi- trarily prescribed sparsity pattern satisfying controllability. Based on this criterion, some novel results on sparsely controlling a system are obtained. It is proven that the minimal number of inputs to guarantee controllability equals to the maximum geometric multiplicity of the STM under the constraint that some states are actuated-forbidden, extending the results of [28]. The minimal sparsity of input matrices with a fixed number of inputs is not necessarily equal to the minimal number of actuated states to ensure controllability. Furthermore, a graphic sub- modular function is built, leading to a greedy algorithm to efficiently approximate the minimal actuated states to assure controllability for general STMs. For the problem of approximating the sparsest input matrices with a fixed number of inputs, we propose a simple greedy algo- rithm (non-submodular) and a two-stage algorithm, and demonstrate that the latter algorithm, inspired from techniques in dynamic coloring, has a provable approximation guarantee. Finally, we present numerical results to show the efficiency and effectiveness of our approaches.Comment: to appear in International Journal of Contro