1,298 research outputs found
An Empirical Analysis of Search in GSAT
We describe an extensive study of search in GSAT, an approximation procedure
for propositional satisfiability. GSAT performs greedy hill-climbing on the
number of satisfied clauses in a truth assignment. Our experiments provide a
more complete picture of GSAT's search than previous accounts. We describe in
detail the two phases of search: rapid hill-climbing followed by a long plateau
search. We demonstrate that when applied to randomly generated 3SAT problems,
there is a very simple scaling with problem size for both the mean number of
satisfied clauses and the mean branching rate. Our results allow us to make
detailed numerical conjectures about the length of the hill-climbing phase, the
average gradient of this phase, and to conjecture that both the average score
and average branching rate decay exponentially during plateau search. We end by
showing how these results can be used to direct future theoretical analysis.
This work provides a case study of how computer experiments can be used to
improve understanding of the theoretical properties of algorithms.Comment: See http://www.jair.org/ for any accompanying file
Allocation in Practice
How do we allocate scarcere sources? How do we fairly allocate costs? These
are two pressing challenges facing society today. I discuss two recent projects
at NICTA concerning resource and cost allocation. In the first, we have been
working with FoodBank Local, a social startup working in collaboration with
food bank charities around the world to optimise the logistics of collecting
and distributing donated food. Before we can distribute this food, we must
decide how to allocate it to different charities and food kitchens. This gives
rise to a fair division problem with several new dimensions, rarely considered
in the literature. In the second, we have been looking at cost allocation
within the distribution network of a large multinational company. This also has
several new dimensions rarely considered in the literature.Comment: To appear in Proc. of 37th edition of the German Conference on
Artificial Intelligence (KI 2014), Springer LNC
Trying again to fail-first
For constraint satisfaction problems (CSPs), Haralick and Elliott [1] introduced the Fail-First Principle and defined in it terms of minimizing branch depth. By devising a range of variable ordering heuristics, each in turn trying harder to fail first, Smith and Grant [2] showed that adherence to this strategy does not guarantee reduction in search effort. The present work builds on Smith and Grant. It benefits from the development of a new framework for characterizing heuristic performance that defines two policies, one concerned with enhancing the likelihood of correctly extending a partial solution, the other with minimizing the effort to prove insolubility. The Fail-First Principle can be restated as calling for adherence to the second, fail-first policy, while discounting the other, promise policy. Our work corrects some deficiencies in the work of Smith and Grant, and goes on to confirm their finding that the Fail-First Principle, as originally defined, is insufficient. We then show that adherence to the fail-first policy must be measured in terms of size of insoluble subtrees, not branch depth. We also show that for soluble problems, both policies must be considered in evaluating heuristic performance. Hence, even in its proper form the Fail-First Principle is insufficient. We also show that the āFFā series of heuristics devised by Smith and Grant is a powerful tool for evaluating heuristic performance, including the subtle relations between heuristic features and adherence to a policy
Mean Curvature Flow of Spacelike Graphs
We prove the mean curvature flow of a spacelike graph in of a map from a closed Riemannian
manifold with to a complete Riemannian manifold
with bounded curvature tensor and derivatives, and with
sectional curvatures satisfying , remains a spacelike graph,
exists for all time, and converges to a slice at infinity. We also show, with
no need of the assumption , that if , or if and
, constant, any map is trivially
homotopic provided where
, in case , and
in case . This largely extends some known results for
constant and compact, obtained using the Riemannian structure
of , and also shows how regularity theory on the mean
curvature flow is simpler and more natural in pseudo-Riemannian setting then in
the Riemannian one.Comment: version 5: Math.Z (online first 30 July 2010). version 4: 30 pages:
we replace the condition by the the weaker one .
The proofs are essentially the same. We change the title to a shorter one. We
add an applicatio
Pathway choice in DNA double strand break repair: Observations of a balancing act
Proper repair of DNA double strand breaks (DSBs) is vital for the preservation of genomic integrity. There are two main pathways that repair DSBs, Homologous recombination (HR) and Non-homologous end-joining (NHEJ). HR is restricted to the S and G2 phases of the cell cycle due to the requirement for the sister chromatid as a template, while NHEJ is active throughout the cell cycle and does not rely on a template. The balance between both pathways is essential for genome stability and numerous assays have been developed to measure the efficiency of the two pathways. Several proteins are known to affect the balance between HR and NHEJ and the complexity of the break also plays a role. In this review we describe several repair assays to determine the efficiencies of both pathways. We discuss how disturbance of the balance between HR and NHEJ can lead to disease, but also how it can be exploited for cancer treatment
Scalable Parallel Numerical Constraint Solver Using Global Load Balancing
We present a scalable parallel solver for numerical constraint satisfaction
problems (NCSPs). Our parallelization scheme consists of homogeneous worker
solvers, each of which runs on an available core and communicates with others
via the global load balancing (GLB) method. The parallel solver is implemented
with X10 that provides an implementation of GLB as a library. In experiments,
several NCSPs from the literature were solved and attained up to 516-fold
speedup using 600 cores of the TSUBAME2.5 supercomputer.Comment: To be presented at X10'15 Worksho
Backbone Fragility and the Local Search Cost Peak
The local search algorithm WSat is one of the most successful algorithms for
solving the satisfiability (SAT) problem. It is notably effective at solving
hard Random 3-SAT instances near the so-called `satisfiability threshold', but
still shows a peak in search cost near the threshold and large variations in
cost over different instances. We make a number of significant contributions to
the analysis of WSat on high-cost random instances, using the
recently-introduced concept of the backbone of a SAT instance. The backbone is
the set of literals which are entailed by an instance. We find that the number
of solutions predicts the cost well for small-backbone instances but is much
less relevant for the large-backbone instances which appear near the threshold
and dominate in the overconstrained region. We show a very strong correlation
between search cost and the Hamming distance to the nearest solution early in
WSat's search. This pattern leads us to introduce a measure of the backbone
fragility of an instance, which indicates how persistent the backbone is as
clauses are removed. We propose that high-cost random instances for local
search are those with very large backbones which are also backbone-fragile. We
suggest that the decay in cost beyond the satisfiability threshold is due to
increasing backbone robustness (the opposite of backbone fragility). Our
hypothesis makes three correct predictions. First, that the backbone robustness
of an instance is negatively correlated with the local search cost when other
factors are controlled for. Second, that backbone-minimal instances (which are
3-SAT instances altered so as to be more backbone-fragile) are unusually hard
for WSat. Third, that the clauses most often unsatisfied during search are
those whose deletion has the most effect on the backbone. In understanding the
pathologies of local search methods, we hope to contribute to the development
of new and better techniques
On The Complexity and Completeness of Static Constraints for Breaking Row and Column Symmetry
We consider a common type of symmetry where we have a matrix of decision
variables with interchangeable rows and columns. A simple and efficient method
to deal with such row and column symmetry is to post symmetry breaking
constraints like DOUBLELEX and SNAKELEX. We provide a number of positive and
negative results on posting such symmetry breaking constraints. On the positive
side, we prove that we can compute in polynomial time a unique representative
of an equivalence class in a matrix model with row and column symmetry if the
number of rows (or of columns) is bounded and in a number of other special
cases. On the negative side, we show that whilst DOUBLELEX and SNAKELEX are
often effective in practice, they can leave a large number of symmetric
solutions in the worst case. In addition, we prove that propagating DOUBLELEX
completely is NP-hard. Finally we consider how to break row, column and value
symmetry, correcting a result in the literature about the safeness of combining
different symmetry breaking constraints. We end with the first experimental
study on how much symmetry is left by DOUBLELEX and SNAKELEX on some benchmark
problems.Comment: To appear in the Proceedings of the 16th International Conference on
Principles and Practice of Constraint Programming (CP 2010
Random Costs in Combinatorial Optimization
The random cost problem is the problem of finding the minimum in an
exponentially long list of random numbers. By definition, this problem cannot
be solved faster than by exhaustive search. It is shown that a classical
NP-hard optimization problem, number partitioning, is essentially equivalent to
the random cost problem. This explains the bad performance of heuristic
approaches to the number partitioning problem and allows us to calculate the
probability distributions of the optimum and sub-optimum costs.Comment: 4 pages, Revtex, 2 figures (eps), submitted to PR
Phase Transition in the Number Partitioning Problem
Number partitioning is an NP-complete problem of combinatorial optimization.
A statistical mechanics analysis reveals the existence of a phase transition
that separates the easy from the hard to solve instances and that reflects the
pseudo-polynomiality of number partitioning. The phase diagram and the value of
the typical ground state energy are calculated.Comment: minor changes (references, typos and discussion of results
- ā¦