5,292 research outputs found
Reachability and Distances under Multiple Changes
Recently it was shown that the transitive closure of a directed graph can be updated using first-order formulas after insertions and deletions of single edges in the dynamic descriptive complexity framework by Dong, Su, and Topor, and Patnaik and Immerman. In other words, Reachability is in DynFO.
In this article we extend the framework to changes of multiple edges at a time, and study the Reachability and Distance queries under these changes. We show that the former problem can be maintained in DynFO(+, x) under changes affecting O({log n}/{log log n}) nodes, for graphs with n nodes. If the update formulas may use a majority quantifier then both Reachability and Distance can be maintained under changes that affect O(log^c n) nodes, for fixed c in N. Some preliminary results towards showing that distances are in DynFO are discussed
Efficient Computation of Multiple Density-Based Clustering Hierarchies
HDBSCAN*, a state-of-the-art density-based hierarchical clustering method,
produces a hierarchical organization of clusters in a dataset w.r.t. a
parameter mpts. While the performance of HDBSCAN* is robust w.r.t. mpts in the
sense that a small change in mpts typically leads to only a small or no change
in the clustering structure, choosing a "good" mpts value can be challenging:
depending on the data distribution, a high or low value for mpts may be more
appropriate, and certain data clusters may reveal themselves at different
values of mpts. To explore results for a range of mpts values, however, one has
to run HDBSCAN* for each value in the range independently, which is
computationally inefficient. In this paper, we propose an efficient approach to
compute all HDBSCAN* hierarchies for a range of mpts values by replacing the
graph used by HDBSCAN* with a much smaller graph that is guaranteed to contain
the required information. An extensive experimental evaluation shows that with
our approach one can obtain over one hundred hierarchies for the computational
cost equivalent to running HDBSCAN* about 2 times.Comment: A short version of this paper appears at IEEE ICDM 2017. Corrected
typos. Revised abstrac
TopCom: Index for Shortest Distance Query in Directed Graph
Finding shortest distance between two vertices in a graph is an important
problem due to its numerous applications in diverse domains, including
geo-spatial databases, social network analysis, and information retrieval.
Classical algorithms (such as, Dijkstra) solve this problem in polynomial time,
but these algorithms cannot provide real-time response for a large number of
bursty queries on a large graph. So, indexing based solutions that pre-process
the graph for efficiently answering (exactly or approximately) a large number
of distance queries in real-time is becoming increasingly popular. Existing
solutions have varying performance in terms of index size, index building time,
query time, and accuracy. In this work, we propose T OP C OM , a novel
indexing-based solution for exactly answering distance queries. Our experiments
with two of the existing state-of-the-art methods (IS-Label and TreeMap) show
the superiority of T OP C OM over these two methods considering scalability and
query time. Besides, indexing of T OP C OM exploits the DAG (directed acyclic
graph) structure in the graph, which makes it significantly faster than the
existing methods if the SCCs (strongly connected component) of the input graph
are relatively small
Planning Graph Heuristics for Belief Space Search
Some recent works in conditional planning have proposed reachability
heuristics to improve planner scalability, but many lack a formal description
of the properties of their distance estimates. To place previous work in
context and extend work on heuristics for conditional planning, we provide a
formal basis for distance estimates between belief states. We give a definition
for the distance between belief states that relies on aggregating underlying
state distance measures. We give several techniques to aggregate state
distances and their associated properties. Many existing heuristics exhibit a
subset of the properties, but in order to provide a standardized comparison we
present several generalizations of planning graph heuristics that are used in a
single planner. We compliment our belief state distance estimate framework by
also investigating efficient planning graph data structures that incorporate
BDDs to compute the most effective heuristics.
We developed two planners to serve as test-beds for our investigation. The
first, CAltAlt, is a conformant regression planner that uses A* search. The
second, POND, is a conditional progression planner that uses AO* search. We
show the relative effectiveness of our heuristic techniques within these
planners. We also compare the performance of these planners with several state
of the art approaches in conditional planning
Faster Algorithms for Weighted Recursive State Machines
Pushdown systems (PDSs) and recursive state machines (RSMs), which are
linearly equivalent, are standard models for interprocedural analysis. Yet RSMs
are more convenient as they (a) explicitly model function calls and returns,
and (b) specify many natural parameters for algorithmic analysis, e.g., the
number of entries and exits. We consider a general framework where RSM
transitions are labeled from a semiring and path properties are algebraic with
semiring operations, which can model, e.g., interprocedural reachability and
dataflow analysis problems.
Our main contributions are new algorithms for several fundamental problems.
As compared to a direct translation of RSMs to PDSs and the best-known existing
bounds of PDSs, our analysis algorithm improves the complexity for
finite-height semirings (that subsumes reachability and standard dataflow
properties). We further consider the problem of extracting distance values from
the representation structures computed by our algorithm, and give efficient
algorithms that distinguish the complexity of a one-time preprocessing from the
complexity of each individual query. Another advantage of our algorithm is that
our improvements carry over to the concurrent setting, where we improve the
best-known complexity for the context-bounded analysis of concurrent RSMs.
Finally, we provide a prototype implementation that gives a significant
speed-up on several benchmarks from the SLAM/SDV project
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