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## Section: New Results

### Co-linear chaining on graphs

We reported the first algorithm that perform co-linear chaining between a sequence and a directed acyclic graph (DAG) [9]. This work concerns dynamic programming algorithms and sequencing alignment. The problem of co-linear chaining is a classical bioinformatics problem, which has immediate application to sequence alignment, as it is used as a filter remove spurious alignment seeds. Co-linear chaining is typically solved using a simple dynamic programming algorithm. Yet, representations of genomes using graphs instead of sequences have recently became an active research topic. As a results, the problem of aligning a sequence to a sequence graph merits consideration. This work provides the first step towards tackling practical sequence-to-graph alignment instances, by first considering the case when the graph is a DAG. We designed a $O\left(k|E|log|V|\right)$ algorithm to solve co-linear chaining on DAGs, which matches the optimal solution for the classical sequence variant, i.e. when the graph is a path.