3,224 research outputs found
Distributed Processing of Generalized Graph-Pattern Queries in SPARQL 1.1
We propose an efficient and scalable architecture for processing generalized
graph-pattern queries as they are specified by the current W3C recommendation
of the SPARQL 1.1 "Query Language" component. Specifically, the class of
queries we consider consists of sets of SPARQL triple patterns with labeled
property paths. From a relational perspective, this class resolves to
conjunctive queries of relational joins with additional graph-reachability
predicates. For the scalable, i.e., distributed, processing of this kind of
queries over very large RDF collections, we develop a suitable partitioning and
indexing scheme, which allows us to shard the RDF triples over an entire
cluster of compute nodes and to process an incoming SPARQL query over all of
the relevant graph partitions (and thus compute nodes) in parallel. Unlike most
prior works in this field, we specifically aim at the unified optimization and
distributed processing of queries consisting of both relational joins and
graph-reachability predicates. All communication among the compute nodes is
established via a proprietary, asynchronous communication protocol based on the
Message Passing Interface
Fast Distributed Approximation for Max-Cut
Finding a maximum cut is a fundamental task in many computational settings.
Surprisingly, it has been insufficiently studied in the classic distributed
settings, where vertices communicate by synchronously sending messages to their
neighbors according to the underlying graph, known as the or
models. We amend this by obtaining almost optimal
algorithms for Max-Cut on a wide class of graphs in these models. In
particular, for any , we develop randomized approximation
algorithms achieving a ratio of to the optimum for Max-Cut on
bipartite graphs in the model, and on general graphs in the
model.
We further present efficient deterministic algorithms, including a
-approximation for Max-Dicut in our models, thus improving the best known
(randomized) ratio of . Our algorithms make non-trivial use of the greedy
approach of Buchbinder et al. (SIAM Journal on Computing, 2015) for maximizing
an unconstrained (non-monotone) submodular function, which may be of
independent interest
Partitioning Perfect Graphs into Stars
The partition of graphs into "nice" subgraphs is a central algorithmic
problem with strong ties to matching theory. We study the partitioning of
undirected graphs into same-size stars, a problem known to be NP-complete even
for the case of stars on three vertices. We perform a thorough computational
complexity study of the problem on subclasses of perfect graphs and identify
several polynomial-time solvable cases, for example, on interval graphs and
bipartite permutation graphs, and also NP-complete cases, for example, on grid
graphs and chordal graphs.Comment: Manuscript accepted to Journal of Graph Theor
Walking Through Waypoints
We initiate the study of a fundamental combinatorial problem: Given a
capacitated graph , find a shortest walk ("route") from a source to a destination that includes all vertices specified by a set
: the \emph{waypoints}. This waypoint routing problem
finds immediate applications in the context of modern networked distributed
systems. Our main contribution is an exact polynomial-time algorithm for graphs
of bounded treewidth. We also show that if the number of waypoints is
logarithmically bounded, exact polynomial-time algorithms exist even for
general graphs. Our two algorithms provide an almost complete characterization
of what can be solved exactly in polynomial-time: we show that more general
problems (e.g., on grid graphs of maximum degree 3, with slightly more
waypoints) are computationally intractable
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