Non-adaptive Group Testing on Graphs

Grebinski and Kucherov (1998) and Alon et al. (2004-2005) study the problem of learning a hidden graph for some especial cases, such as hamiltonian cycle, cliques, stars, and matchings. This problem is motivated by problems in chemical reactions, molecular biology and genome sequencing. In this paper, we present a generalization of this problem. Precisely, we consider a graph G and a subgraph H of G and we assume that G contains exactly one defective subgraph isomorphic to H. The goal is to find the defective subgraph by testing whether an induced subgraph contains an edge of the defective subgraph, with the minimum number of tests. We present an upper bound for the number of tests to find the defective subgraph by using the symmetric and high probability variation of Lov\'asz Local Lemma

Spectral Relaxations and Fair Densest Subgraphs

Reducing hidden bias in the data and ensuring fairness in algorithmic data analysis has recently received significant attention. In this paper, we address the problem of identifying a densest subgraph, while ensuring that none of one binary protected attribute is disparately impacted. Unfortunately, the underlying algorithmic problem is NP-hard, even in its approximation version: approximating the densest fair subgraph with a polynomial-time algorithm is at least as hard as the densest subgraph problem of at most k vertices, for which no constant approximation algorithms are known. Despite such negative premises, we are able to provide approximation results in two important cases. In particular, we are able to prove that a suitable spectral embedding allows recovery of an almost optimal, fair, dense subgraph hidden in the input data, whenever one is present, a result that is further supported by experimental evidence. We also show a polynomial-time, $2$-approximation algorithm, whenever the underlying graph is itself fair. We finally prove that, under the small set expansion hypothesis, this result is tight for fair graphs. The above theoretical findings drive the design of heuristics, which we experimentally evaluate on a scenario based on real data, in which our aim is to strike a good balance between diversity and highly correlated items from Amazon co-purchasing graphs

Subgraph adaptive structure-aware graph contrastive learning

Graph contrastive learning (GCL) has been subject to more attention and been widely applied to numerous graph learning tasks such as node classification and link prediction. Although it has achieved great success and even performed better than supervised methods in some tasks, most of them depend on node-level comparison, while ignoring the rich semantic information contained in graph topology, especially for social networks. However, a higher-level comparison requires subgraph construction and encoding, which remain unsolved. To address this problem, we propose a subgraph adaptive structure-aware graph contrastive learning method (PASCAL) in this work, which is a subgraph-level GCL method. In PASCAL, we construct subgraphs by merging all motifs that contain the target node. Then we encode them on the basis of motif number distribution to capture the rich information hidden in subgraphs. By incorporating motif information, PASCAL can capture richer semantic information hidden in local structures compared with other GCL methods. Extensive experiments on six benchmark datasets show that PASCAL outperforms state-of-art graph contrastive learning and supervised methods in most cases

Seeing the Unseen Network: Inferring Hidden Social Ties from Respondent-Driven Sampling

Learning about the social structure of hidden and hard-to-reach populations --- such as drug users and sex workers --- is a major goal of epidemiological and public health research on risk behaviors and disease prevention. Respondent-driven sampling (RDS) is a peer-referral process widely used by many health organizations, where research subjects recruit other subjects from their social network. In such surveys, researchers observe who recruited whom, along with the time of recruitment and the total number of acquaintances (network degree) of respondents. However, due to privacy concerns, the identities of acquaintances are not disclosed. In this work, we show how to reconstruct the underlying network structure through which the subjects are recruited. We formulate the dynamics of RDS as a continuous-time diffusion process over the underlying graph and derive the likelihood for the recruitment time series under an arbitrary recruitment time distribution. We develop an efficient stochastic optimization algorithm called RENDER (REspoNdent-Driven nEtwork Reconstruction) that finds the network that best explains the collected data. We support our analytical results through an exhaustive set of experiments on both synthetic and real data.Comment: A full version with technical proofs. Accepted by AAAI-1

A Cross-Layer Design Based on Geographic Information for Cooperative Wireless Networks

Most of geographic routing approaches in wireless ad hoc and sensor networks do not take into consideration the medium access control (MAC) and physical layers when designing a routing protocol. In this paper, we focus on a cross-layer framework design that exploits the synergies between network, MAC, and physical layers. In the proposed CoopGeo, we use a beaconless forwarding scheme where the next hop is selected through a contention process based on the geographic position of nodes. We optimize this Network-MAC layer interaction using a cooperative relaying technique with a relay selection scheme also based on geographic information in order to improve the system performance in terms of reliability.Comment: in 2010 IEEE 71st Vehicular Technology Conference, 201