Nanson's and Baldwin's voting rules select a winner by successively eliminating candidates with low Borda scores. We show that these rules have a number of desirable computational properties. In particular, with unweighted votes, it is NP-hard to manipulate either rule with one manipulator, whilst with weighted votes, it is NP-hard to manipulate either rule with a small number of candidates and a coalition of manipulators. As only a couple of other voting rules are known to be NP-hard to manipulate with a single manipulator, Nanson's and Baldwin's rules appear to be particularly resistant to manipulation from a theoretical perspective. We also propose a number of approximation methods for manipulating these two rules. Experiments demonstrate that both rules are often difficult to manipulate in practice. These results suggest that elimination style voting rules deserve further study.

We propose an online form of the cake cutting problem. This models situations where agents arrive and depart during the process of dividing a resource. We show that well known fair division procedures like cut-and-choose and the Dubins-Spanier moving knife procedure can be adapted to apply to such online problems. We propose some fairness properties that online cake cutting procedures can possess like online forms of proportionality and envy-freeness. We also consider the impact of collusion between agents. Finally, we study theoretically and empirically the competitive ratio of these online cake cutting procedures. Based on its resistance to collusion, and its good performance in practice, our results favour the online version of the cut-and-choose procedure over the online version of the moving knife procedure.

The automatic generation of decision trees based on off-line reasoning on models of a domain is a reasonable compromise between the advantages of using a model-based approach in technical domains and the constraints imposed by embedded applications. In this paper we extend the approach to deal with temporal information. We introduce a notion of temporal decision tree, which is designed to make use of relevant information as long as it is acquired, and we present an algorithm for compiling such trees from a model-based reasoning system.

Planning with numeric state variables has been a challenge for many years, and was a part of the 3rd International Planning Competition (IPC-3). Currently one of the most popular and successful algorithmic techniques in STRIPS planning is to guide search by a heuristic function, where the heuristic is based on relaxing the planning task by ignoring the delete lists of the available actions. We present a natural extension of ``ignoring delete lists'' to numeric state variables, preserving the relevant theoretical properties of the STRIPS relaxation under the condition that the numeric task at hand is ``monotonic''. We then identify a subset of the numeric IPC-3 competition language, ``linear tasks'', where monotonicity can be achieved by pre-processing. Based on that, we extend the algorithms used in the heuristic planning system FF to linear tasks. The resulting system Metric-FF is, according to the IPC-3 results which we discuss, one of the two currently most efficient numeric planners.

The recent emergence of heavily-optimized modal decision procedures has highlighted the key role of empirical testing in this domain. Unfortunately, the introduction of extensive empirical tests for modal logics is recent, and so far none of the proposed test generators is very satisfactory. To cope with this fact, we present a new random generation method that provides benefits over previous methods for generating empirical tests. It fixes and much generalizes one of the best-known methods, the random CNF_[]m test, allowing for generating a much wider variety of problems, covering in principle the whole input space. Our new method produces much more suitable test sets for the current generation of modal decision procedures. We analyze the features of the new method by means of an extensive collection of empirical tests.

SAPA is a domain-independent heuristic forward chaining planner that can handle durative actions, metric resource constraints, and deadline goals. It is designed to be capable of handling the multi-objective nature of metric temporal planning. Our technical contributions include (i) planning-graph based methods for deriving heuristics that are sensitive to both cost and makespan (ii) techniques for adjusting the heuristic estimates to take action interactions and metric resource limitations into account and (iii) a linear time greedy post-processing technique to improve execution flexibility of the solution plans. An implementation of SAPA using many of the techniques presented in this paper was one of the best domain independent planners for domains with metric and temporal constraints in the third International Planning Competition, held at AIPS-02. We describe the technical details of extracting the heuristics and present an empirical evaluation of the current implementation of SAPA.

The performance of anytime algorithms can be improved by simultaneously solving several instances of algorithm-problem pairs. These pairs may include different instances of a problem (such as starting from a different initial state), different algorithms (if several alternatives exist), or several runs of the same algorithm (for non-deterministic algorithms). In this paper we present a methodology for designing an optimal scheduling policy based on the statistical characteristics of the algorithms involved. We formally analyze the case where the processes share resources (a single-processor model), and provide an algorithm for optimal scheduling. We analyze, theoretically and empirically, the behavior of our scheduling algorithm for various distribution types. Finally, we present empirical results of applying our scheduling algorithm to the Latin Square problem.

Recently, planning based on answer set programming has been proposed as an approach towards realizing declarative planning systems. In this paper, we present the language Kc, which extends the declarative planning language K by action costs. Kc provides the notion of admissible and optimal plans, which are plans whose overall action costs are within a given limit resp. minimum over all plans (i.e., cheapest plans). As we demonstrate, this novel language allows for expressing some nontrivial planning tasks in a declarative way. Furthermore, it can be utilized for representing planning problems under other optimality criteria, such as computing ``shortest'' plans (with the least number of steps), and refinement combinations of cheapest and fastest plans. We study complexity aspects of the language Kc and provide a transformation to logic programs, such that planning problems are solved via answer set programming. Furthermore, we report experimental results on selected problems. Our experience is encouraging that answer set planning may be a valuable approach to expressive planning systems in which intricate planning problems can be naturally specified and solved.

Despite their near dominance, heuristic state search planners still lag behind disjunctive planners in the generation of parallel plans in classical planning. The reason is that directly searching for parallel solutions in state space planners would require the planners to branch on all possible subsets of parallel actions, thus increasing the branching factor exponentially. We present a variant of our heuristic state search planner AltAlt, called AltAltp which generates parallel plans by using greedy online parallelization of partial plans. The greedy approach is significantly informed by the use of novel distance heuristics that AltAltp derives from a graphplan-style planning graph for the problem. While this approach is not guaranteed to provide optimal parallel plans, empirical results show that AltAltp is capable of generating good quality parallel plans at a fraction of the cost incurred by the disjunctive planners.

TALplanner is a forward-chaining planner that relies on domain knowledge in the shape of temporal logic formulas in order to prune irrelevant parts of the search space. TALplanner recently participated in the third International Planning Competition, which had a clear emphasis on increasing the complexity of the problem domains being used as benchmark tests and the expressivity required to represent these domains in a planning system. Like many other planners, TALplanner had support for some but not all aspects of this increase in expressivity, and a number of changes to the planner were required. After a short introduction to TALplanner, this article describes some of the changes that were made before and during the competition. We also describe the process of introducing suitable domain knowledge for several of the competition domains.