Enabling Scalability: Graph Hierarchies and Fault Tolerance

In this dissertation, we explore approaches to two techniques for building scalable algorithms. First, we look at different graph problems. We show how to exploit the input graph's inherent hierarchy for scalable graph algorithms. The second technique takes a step back from concrete algorithmic problems. Here, we consider the case of node failures in large distributed systems and present techniques to quickly recover from these.

In the first part of the dissertation, we investigate how hierarchies in graphs can be used to scale algorithms to large inputs. We develop algorithms for three graph problems based on two approaches to build hierarchies. The first approach reduces instance sizes for NP-hard problems by applying so-called reduction rules. These rules can be applied in polynomial time. They either find parts of the input that can be solved in polynomial time, or they identify structures that can be contracted (reduced) into smaller structures without loss of information for the specific problem. After solving the reduced instance using an exponential-time algorithm, these previously contracted structures can be uncontracted to obtain an exact solution for the original input. ... mehrIn addition to a simple preprocessing procedure, reduction rules can also be used in branch-and-reduce algorithms where they are successively applied after each branching step to build a hierarchy of problem kernels of increasing computational hardness. We develop reduction-based algorithms for the classical NP-hard problems Maximum Independent Set and Maximum Cut. The second approach is used for route planning in road networks where we build a hierarchy of road segments based on their importance for long distance shortest paths. By only considering important road segments when we are far away from the source and destination, we can substantially speed up shortest path queries.

In the second part of this dissertation, we take a step back from concrete graph problems and look at more general problems in high performance computing (HPC). Here, due to the ever increasing size and complexity of HPC clusters, we expect hardware and software failures to become more common in massively parallel computations. We present two techniques for applications to recover from failures and resume computation. Both techniques are based on in-memory storage of redundant information and a data distribution that enables fast recovery. The first technique can be used for general purpose distributed processing frameworks: We identify data that is redundantly available on multiple machines and only introduce additional work for the remaining data that is only available on one machine. The second technique is a checkpointing library engineered for fast recovery using a data distribution method that achieves balanced communication loads. Both our techniques have in common that they work in settings where computation after a failure is continued with less machines than before. This is in contrast to many previous approaches that---in particular for checkpointing---focus on systems that keep spare resources available to replace failed machines.

Overall, we present different techniques that enable scalable algorithms. While some of these techniques are specific to graph problems, we also present tools for fault tolerant algorithms and applications in a distributed setting. To show that those can be helpful in many different domains, we evaluate them for graph problems and other applications like phylogenetic tree inference.