12,603 research outputs found
On Derandomizing Local Distributed Algorithms
The gap between the known randomized and deterministic local distributed
algorithms underlies arguably the most fundamental and central open question in
distributed graph algorithms. In this paper, we develop a generic and clean
recipe for derandomizing LOCAL algorithms. We also exhibit how this simple
recipe leads to significant improvements on a number of problem. Two main
results are:
- An improved distributed hypergraph maximal matching algorithm, improving on
Fischer, Ghaffari, and Kuhn [FOCS'17], and giving improved algorithms for
edge-coloring, maximum matching approximation, and low out-degree edge
orientation. The first gives an improved algorithm for Open Problem 11.4 of the
book of Barenboim and Elkin, and the last gives the first positive resolution
of their Open Problem 11.10.
- An improved distributed algorithm for the Lov\'{a}sz Local Lemma, which
gets closer to a conjecture of Chang and Pettie [FOCS'17], and moreover leads
to improved distributed algorithms for problems such as defective coloring and
-SAT.Comment: 37 page
Optimization Modulo Theories with Linear Rational Costs
In the contexts of automated reasoning (AR) and formal verification (FV),
important decision problems are effectively encoded into Satisfiability Modulo
Theories (SMT). In the last decade efficient SMT solvers have been developed
for several theories of practical interest (e.g., linear arithmetic, arrays,
bit-vectors). Surprisingly, little work has been done to extend SMT to deal
with optimization problems; in particular, we are not aware of any previous
work on SMT solvers able to produce solutions which minimize cost functions
over arithmetical variables. This is unfortunate, since some problems of
interest require this functionality.
In the work described in this paper we start filling this gap. We present and
discuss two general procedures for leveraging SMT to handle the minimization of
linear rational cost functions, combining SMT with standard minimization
techniques. We have implemented the procedures within the MathSAT SMT solver.
Due to the absence of competitors in the AR, FV and SMT domains, we have
experimentally evaluated our implementation against state-of-the-art tools for
the domain of linear generalized disjunctive programming (LGDP), which is
closest in spirit to our domain, on sets of problems which have been previously
proposed as benchmarks for the latter tools. The results show that our tool is
very competitive with, and often outperforms, these tools on these problems,
clearly demonstrating the potential of the approach.Comment: Submitted on january 2014 to ACM Transactions on Computational Logic,
currently under revision. arXiv admin note: text overlap with arXiv:1202.140
Model Counting of Query Expressions: Limitations of Propositional Methods
Query evaluation in tuple-independent probabilistic databases is the problem
of computing the probability of an answer to a query given independent
probabilities of the individual tuples in a database instance. There are two
main approaches to this problem: (1) in `grounded inference' one first obtains
the lineage for the query and database instance as a Boolean formula, then
performs weighted model counting on the lineage (i.e., computes the probability
of the lineage given probabilities of its independent Boolean variables); (2)
in methods known as `lifted inference' or `extensional query evaluation', one
exploits the high-level structure of the query as a first-order formula.
Although it is widely believed that lifted inference is strictly more powerful
than grounded inference on the lineage alone, no formal separation has
previously been shown for query evaluation. In this paper we show such a formal
separation for the first time.
We exhibit a class of queries for which model counting can be done in
polynomial time using extensional query evaluation, whereas the algorithms used
in state-of-the-art exact model counters on their lineages provably require
exponential time. Our lower bounds on the running times of these exact model
counters follow from new exponential size lower bounds on the kinds of d-DNNF
representations of the lineages that these model counters (either explicitly or
implicitly) produce. Though some of these queries have been studied before, no
non-trivial lower bounds on the sizes of these representations for these
queries were previously known.Comment: To appear in International Conference on Database Theory (ICDT) 201
Symmetry Breaking for Answer Set Programming
In the context of answer set programming, this work investigates symmetry
detection and symmetry breaking to eliminate symmetric parts of the search
space and, thereby, simplify the solution process. We contribute a reduction of
symmetry detection to a graph automorphism problem which allows to extract
symmetries of a logic program from the symmetries of the constructed coloured
graph. We also propose an encoding of symmetry-breaking constraints in terms of
permutation cycles and use only generators in this process which implicitly
represent symmetries and always with exponential compression. These ideas are
formulated as preprocessing and implemented in a completely automated flow that
first detects symmetries from a given answer set program, adds
symmetry-breaking constraints, and can be applied to any existing answer set
solver. We demonstrate computational impact on benchmarks versus direct
application of the solver.
Furthermore, we explore symmetry breaking for answer set programming in two
domains: first, constraint answer set programming as a novel approach to
represent and solve constraint satisfaction problems, and second, distributed
nonmonotonic multi-context systems. In particular, we formulate a
translation-based approach to constraint answer set solving which allows for
the application of our symmetry detection and symmetry breaking methods. To
compare their performance with a-priori symmetry breaking techniques, we also
contribute a decomposition of the global value precedence constraint that
enforces domain consistency on the original constraint via the unit-propagation
of an answer set solver. We evaluate both options in an empirical analysis. In
the context of distributed nonmonotonic multi-context system, we develop an
algorithm for distributed symmetry detection and also carry over
symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201
Independent Set, Induced Matching, and Pricing: Connections and Tight (Subexponential Time) Approximation Hardnesses
We present a series of almost settled inapproximability results for three
fundamental problems. The first in our series is the subexponential-time
inapproximability of the maximum independent set problem, a question studied in
the area of parameterized complexity. The second is the hardness of
approximating the maximum induced matching problem on bounded-degree bipartite
graphs. The last in our series is the tight hardness of approximating the
k-hypergraph pricing problem, a fundamental problem arising from the area of
algorithmic game theory. In particular, assuming the Exponential Time
Hypothesis, our two main results are:
- For any r larger than some constant, any r-approximation algorithm for the
maximum independent set problem must run in at least
2^{n^{1-\epsilon}/r^{1+\epsilon}} time. This nearly matches the upper bound of
2^{n/r} (Cygan et al., 2008). It also improves some hardness results in the
domain of parameterized complexity (e.g., Escoffier et al., 2012 and Chitnis et
al., 2013)
- For any k larger than some constant, there is no polynomial time min
(k^{1-\epsilon}, n^{1/2-\epsilon})-approximation algorithm for the k-hypergraph
pricing problem, where n is the number of vertices in an input graph. This
almost matches the upper bound of min (O(k), \tilde O(\sqrt{n})) (by Balcan and
Blum, 2007 and an algorithm in this paper).
We note an interesting fact that, in contrast to n^{1/2-\epsilon} hardness
for polynomial-time algorithms, the k-hypergraph pricing problem admits
n^{\delta} approximation for any \delta >0 in quasi-polynomial time. This puts
this problem in a rare approximability class in which approximability
thresholds can be improved significantly by allowing algorithms to run in
quasi-polynomial time.Comment: The full version of FOCS 201
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