, was introduced by Vladimir Levenshtein two decades ago. While there has been considerable theoretical work on trace reconstruction, practical solutions have only recently started to emerge in the context of two rapidly developing research areas: immunogenomics and DNA data storage. In immunogenomics, traces correspond to mutated copies of genes, with mutations generated naturally by the adaptive immune system. In DNA data storage, traces correspond to noisy copies of DNA molecules that encode digital data, with errors being artifacts of the data retrieval process. In this paper, we introduce several new trace generation models and open questions relevant to trace reconstruction for immunogenomics and DNA data storage, survey theoretical results on trace reconstruction, and highlight their connections to computational biology. Throughout, we discuss the applicability and shortcomings of known solutions and suggest future research directions.

Immunoglobulin genes are formed through V(D)J recombination, which joins the variable (V), diversity (D), and joining (J) germline genes. Since variations in germline genes have been linked to various diseases, personalized immunogenomics focuses on finding alleles of germline genes across various patients. Although reconstruction of V and J genes is a well-studied problem, the more challenging task of reconstructing D genes remained open until the IgScout algorithm was developed in 2019. In this work, we address limitations of IgScout by developing a probabilistic MINING-D algorithm for D gene reconstruction, apply it to hundreds of immunosequencing datasets from multiple species, and validate the newly inferred D genes by analyzing diverse whole genome sequencing datasets and haplotyping heterozygous V genes.

In this paper, we propose algorithms for finding the optimum multi-hop routes and corresponding transmit powers that maximize the throughput between a pair of device-to-device (D2D) nodes, under a constraint on the maximum interference caused to the cellular network. Our solution involves two steps. In the first step, we determine the set of feasible D2D links, based on the interference constraint. In the second step, we use the celebrated Dijkstra's algorithm to find throughput-optimal routes between a given pair of D2D nodes under two scenarios: a) The Fixed Rate Scheme and b) The Fixed Power Scheme. The dependency of the net D2D throughput on the system parameters such as target SINR is analyzed for both the schemes, and a procedure to find the optimum parameter setting is proposed. The performance of the algorithms is illustrated using computer simulations. The results show that, depending on the network topology, a significantly higher throughput can be achieved by using multi-hop paths compared to using single-hop, direct D2D communication.