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

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

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 “FF” 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

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

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

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

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

New scaling for the alpha effect in slowly rotating turbulence

Using simulations of slowly rotating stratified turbulence, we show that the alpha effect responsible for the generation of astrophysical magnetic fields is proportional to the logarithmic gradient of kinetic energy density rather than that of momentum, as was previously thought. This result is in agreement with a new analytic theory developed in this paper for large Reynolds numbers. Thus, the contribution of density stratification is less important than that of turbulent velocity. The alpha effect and other turbulent transport coefficients are determined by means of the test-field method. In addition to forced turbulence, we also investigate supernova-driven turbulence and stellar convection. In some cases (intermediate rotation rate for forced turbulence, convection with intermediate temperature stratification, and supernova-driven turbulence) we find that the contribution of density stratification might be even less important than suggested by the analytic theory.Comment: 10 pages, 9 figures, revised version, Astrophys. J., in pres

Theory Learning with Symmetry Breaking

This paper investigates the use of a Prolog coded SMT solver in tackling a well known constraints problem, namely packing a given set of consecutive squares into a given rectangle, and details the developments in the solver that this motivates. The packing problem has a natural model in the theory of quantifier-free integer difference logic, a theory supported by many SMT solvers. The solver used in this work exploits a data structure consisting of an incremental Floyd-Warshall matrix paired with a watch matrix that monitors the entailment status of integer difference constraints. It is shown how this structure can be used to build unsatisfiable theory cores on the fly, which in turn allows theory learning to be incorporated into the solver. Further, it is shown that a problem-specific and non-standard approach to learning can be taken where symmetry breaking is incorporated into the learning stage, magnifying the effect of learning. It is argued that the declarative framework allows the solver to be used in this white box manner and is a strength of the solver. The approach is experimentally evaluated