Parallel Graph Algorithms in Constant Adaptive Rounds: Theory meets Practice

We study fundamental graph problems such as graph connectivity, minimum spanning forest (MSF), and approximate maximum (weight) matching in a distributed setting. In particular, we focus on the Adaptive Massively Parallel Computation (AMPC) model, which is a theoretical model that captures MapReduce-like computation augmented with a distributed hash table. We show the first AMPC algorithms for all of the studied problems that run in a constant number of rounds and use only $O(n^\epsilon)$ space per machine, where $0 < \epsilon < 1$. Our results improve both upon the previous results in the AMPC model, as well as the best-known results in the MPC model, which is the theoretical model underpinning many popular distributed computation frameworks, such as MapReduce, Hadoop, Beam, Pregel and Giraph. Finally, we provide an empirical comparison of the algorithms in the MPC and AMPC models in a fault-tolerant distriubted computation environment. We empirically evaluate our algorithms on a set of large real-world graphs and show that our AMPC algorithms can achieve improvements in both running time and round-complexity over optimized MPC baselines

Approximation algorithms for network design and cut problems in bounded-treewidth

This thesis explores two optimization problems, the group Steiner tree and firefighter problems, which are known to be NP-hard even on trees. We study the approximability of these problems on trees and bounded-treewidth graphs. In the group Steiner tree, the input is a graph and sets of vertices called groups; the goal is to choose one representative from each group and connect all the representatives with minimum cost. We show an O(log^2 n)-approximation algorithm for bounded-treewidth graphs, matching the known lower bound for trees, and improving the best possible result using previous techniques. We also show improved approximation results for group Steiner forest, directed Steiner forest, and a fault-tolerant version of group Steiner tree. In the firefighter problem, we are given a graph and a vertex which is burning. At each time step, we can protect one vertex that is not burning; fire then spreads to all unprotected neighbors of burning vertices. The goal is to maximize the number of vertices that the fire does not reach. On trees, a classic (1-1/e)-approximation algorithm is known via LP rounding. We prove that the integrality gap of the LP matches this approximation, and show significant evidence that additional constraints may improve its integrality gap. On bounded-treewidth graphs, we show that it is NP-hard to find a subpolynomial approximation even on graphs of treewidth 5. We complement this result with an O(1)-approximation on outerplanar graphs.Diese Arbeit untersucht zwei Optimierungsprobleme, von welchen wir wissen, dass sie selbst in Bäumen NP-schwer sind. Wir analysieren Approximationen für diese Probleme in Bäumen und Graphen mit begrenzter Baumweite. Im Gruppensteinerbaumproblem, sind ein Graph und Mengen von Knoten (Gruppen) gegeben; das Ziel ist es, einen Knoten von jeder Gruppe mit minimalen Kosten zu verbinden. Wir beschreiben einen O(log^2 n)-Approximationsalgorithmus für Graphen mit beschränkter Baumweite, dies entspricht der zuvor bekannten unteren Schranke für Bäume und ist zudem eine Verbesserung über die bestmöglichen Resultate die auf anderen Techniken beruhen. Darüber hinaus zeigen wir verbesserte Approximationsresultate für andere Gruppensteinerprobleme. Im Feuerwehrproblem sind ein Graph zusammen mit einem brennenden Knoten gegeben. In jedem Zeitschritt können wir einen Knoten der noch nicht brennt auswählen und diesen vor dem Feuer beschützen. Das Feuer breitet sich anschließend zu allen Nachbarn aus. Das Ziel ist es die Anzahl der Knoten die vom Feuer unberührt bleiben zu maximieren. In Bäumen existiert ein lang bekannter (1-1/e)-Approximationsalgorithmus der auf LP Rundung basiert. Wir zeigen, dass die Ganzzahligkeitslücke des LP tatsächlich dieser Approximation entspricht, und dass weitere Einschränkungen die Ganzzahligkeitslücke möglicherweise verbessern könnten. Für Graphen mit beschränkter Baumweite zeigen wir, dass es NP-schwer ist, eine sub-polynomielle Approximation zu finden

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Efficient Passive Clustering and Gateways selection MANETs

Passive clustering does not employ control packets to collect topological information in ad hoc networks. In our proposal, we avoid making frequent changes in cluster architecture due to repeated election and re-election of cluster heads and gateways. Our primary objective has been to make Passive Clustering more practical by employing optimal number of gateways and reduce the number of rebroadcast packets

Interconnect yield analysis and fault tolerance for field programmable gate arrays

Imperial Users onl

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum