16108034
Interleaved and Discrepancy Based Search
We present a detailed experimental comparison of interleaved depth-rst search and depth-bounded discrepancy search, two tree search procedures recently developed with the same goal: to reduce the cost of heuristic mistakes at the top of the tree. Our comparison uses an abstract heur-istic model, and three diierent concrete problem classes: binary constraint satisfaction, quasigroup completion and number partitioning problems. Results indicate that both search strategies often reduce search. In addition, they show that their eeciency depends on a trade-oo between the number of discrepancies (branch points against the heuristic) considered at the top of the tree, and the overhead of expanding branches from these discrepancies. If the number of discrepancies is large, the overhead can outweigh the beneets.
12061015
Automatic Invention of Integer Sequences
We report on the application of the HR program (Colton, Bundy, & Walsh 1999) to the problem of automatically inventing integer sequences. Seventeen sequences invented by HR are interesting enough to have been accepted into the Encyclopedia of Integer Sequences (Sloane 2000) and all were supplied with interesting conjectures about their nature, also discovered by HR. By extending HR, we have enabled it to perform a two stage process of invention and investigation. This involves generating both the definition and terms of a new sequence, relating it to sequences already in the Encyclopedia and pruning the output to help identify the most surprising and interesting results.
5055655
The Complexity of Global Constraints
We study the computational complexity of reasoning with global constraints. We show that reasoning with such constraints is intractable in general. We then demonstrate how the same tools of computational complexity can be used in the design and analysis of specific global constraints. In particular, we illustrate how computational complexity can be used to determine when a lesser level of local consistency should be enforced, when decomposing constraints will lose pruning, and when combining constraints is tractable. We also show how the same tools can be used to study symmetry breaking, meta-constraints like the cardinality constraint, and learning nogoods.
2156641
Multiset Ordering Constraints
We identify a new and important global (or nonbinary) constraint which ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different applications including breaking symmetry and fuzzy constraint satisfaction. We propose and implement a linear time algorithm for enforcing generalised arc-consistency on such a multiset ordering constraint. Experimental results show considerable promise.
17485829
Beyond Finite Domains: The All Different and Global Cardinality Constraints
We describe how the propagator for the ALL-DIFFERENT constraint can be generalized to prune variables whose domains are not just simple finite integer domains. We show, for example, how it can be used to propagate set, multiset and tuple variables.
11070611
The Constrainedness of Arc Consistency
We show that the same methodology used to study phase transition behaviour in NP-complete problems works with a polynomial problem class: establishing arc consistency. A general measure of the constrainedness of an ensemble of problems, used to locate phase transitions in random NP-complete problems, predicts the location of a phase transition in establishing arc consistency. A complexity peak for the AC3 algorithm is associated with this transition. Finite size scaling models both the scaling of this transition and the computational cost. On problems at the phase transition, this model of computational cost agrees with the theoretical worst case. As with NP-complete problems, constrainedness — and proxies for it which are cheaper to compute — can be used as a heuristic for reducing the number of checks needed to establish arc consistency in AC3. 
 
The authors are supported by EPSRC awards GR/L/24014 and GR/K/65706, and the EU award EU20603. The authors wish to thank other members of the APES research group for their help, and Gene Freuder.
18489826
Counting unrooted loopless planar maps
We present a formula for the number of n-edge unrooted loopless planar maps considered up to orientation-preserving isomorphism. The only sum contained in this formula is over the divisors of n.
1960492
Challenges in securing voice over IP
Although VoIP offers lower cost and greater flexibility, it can also introduce significant risks and vulnerabilities. This article explains the challenges of VoIP security and outlines steps for helping to secure an organization's VoIP network.
8458935
Efficient enumeration of sensed planar maps
We use Liskovets' quotient maps and Robinson's cycle index sums to count 1-, 2- and 3-connected planar maps by number of vertices and edges up to sense-preserving homeomorphism of the embedding sphere. Although Wormald has already counted these maps up to all homeomorphism, sense-reversing as well as sense-preserving, our methods are computationally more efficient for counting these maps up to orientation-preserving homeomorphism and yield closed-form enumeration formulas in the case of 1- and 2-connected maps. Our formula for 1-connected planar maps uses the number of rooted planar maps with i+1 vertices and j+1 faces; we evaluate these numbers using a method that is more efficient than substituting into Tutte's parametric equations, and we also count rooted toroidal maps by number of vertices and faces more efficiently than by substituting into Arques' explicit formula.
14691140
Counting unlabelled three-connected and homeomorphically irreducible two-connected graphs
A graph will be assumed to be finite and unoriented, with no loops or multiple edges; if multiple edges are to be allowed, the term multigraph will be used. A graph or multigraph. will be called k-connected if at least k vertices and their incident edges must be removed to disconnect it (a complete graph is considered to be k-connected for any k). A block (respectively, multiblock) is a 2-connected graph (respectively, multigraph) with at least 2 vertices, and a brick is a 3-connected graph with at least 4 vertices. A Iabelling of a graph or multigraph with n vertices is a l-l correspondence from the set { 1, 2,..., n} onto the set of its vertices. Let A(x, y) be the mixed exponential generating function C,,, An,,,,x”.vmln!, where A,,, is the number of labelled graphs with n vertices and m edges, and let C(x, y) and B(x, y) be analogous generating functions which count labelled connected graphs and labelled blocks, respectively. The following formulae, due to Riddell [lo], appear in one-variable form in [6, pp. 3-111:
3106079
Efficient Exploration With Latent Structure
When interacting with a new environment, a robot can improve its online performance by efficiently exploring the effects of its actions. The efficiency of exploration can be expanded significantly by modeling and using latent structure to generalize experiences. We provide a theoretical development of the problem of exploration with latent structure, analyze several algorithms and prove matching lower bounds. We demonstrate our algorithmic ideas on a simple robot car repeatedly traversing a path with two different surface properties.