I present several computational complexity results for propositional STRIPS planning, i.e., STRIPS planning restricted to ground formulas. Different planning problems can be defined by restricting the type of formulas, placing limits on the number of pre- and postconditions, by restricting negation in pre- and postconditions, and by requiring optimal plans. For these types of restrictions, I show when planning is tractable (polynomial) and intractable (NPhard) . In general, it is PSPACE-complete to determine if a given planning instance has any solutions. Extremely severe restrictions on both the operators and the formulas are required to guarantee polynomial time or even NP-completeness. For example, when only ground literals are permitted, determining plan existence is PSPACE-complete even if operators are limited to two preconditions and two postconditions. When definite Horn ground formulas are permitted, determining plan existence is PSPACE-complete even if operators are limited t...

Consider a set of parties who do not trust each other, nor the channels by which they communicate. Still, the parties wish to correctly compute some common function of their local inputs, while keeping their local data as private as possible. This, in a nutshell, is the problem of secure multiparty computation. This problem is fundamental in cryptography and in the study of distributed computations. It takes many different forms, depending on the underlying network, on the function to be computed, and on the amount of distrust the parties have in each other and in the network. We study several aspects of secure multiparty computation. We first present new definitions of this problem in various settings. Our definitions draw from previous ideas and formalizations, and incorporate aspects that were previously overlooked. Next we study the problem of dealing with adaptive adversaries. (Adaptive adversaries are adversaries that corrupt parties during the course of the computation, based on...

A multiparty interaction is a set of I/O actions executed jointly by a number of processes, each of which must be ready to execute its own action for any of the actions in the set to occur. An attempt to participate in an interaction delays a process until all other participants are available. Although a relatively new concept, the multiparty interaction has found its way into a number of distributed programming languages and algebraic models of concurrency. In this paper, we present a taxonomy of languages for multiparty interaction that covers all proposals of which we are aware. Based on this taxonomy, we then present a comprehensive analysis of the computational complexity of the multiparty interaction scheduling problem, the problem of scheduling multiparty interactions in a given execution environment. 1 Introduction A multiparty interaction is a set of I/O actions executed jointly by a number of processes, each of which must be ready to execute its own action for any of the act...

Multilevel strategies have proven to be very powerful approaches in order to partition graphs efficiently. Their efficiency is dominated by two parts; the coarsening and the local improvement strategies. Several methods have been developed to solve these problems, but their efficiency has only been proven on an experimental basis. In this paper we present new and efficient methods for both problems, while satisfying certain quality measurements. For the coarsening part we develop a new approximation algorithm for maximum weighted matching in general edge-weighted graphs. It calculates a matching with an edge weight of at least 1 2 of the edge weight of a maximum weighted matching. Its time complexity is O(jEj), with jEj being the number of edges in the graph. Furthermore, we use the Helpful-Set strategy for the local improvement of partitions. For partitioning graphs with a regular degree of 2k into 2 parts, it guarantees an upper bound of k\Gamma1 2 jV j + 1 on the cut size of th...

A new approximation algorithm for maximum weighted matching in general edge-weighted graphs is presented. It calculates a matching with an edge weight of at least 1/2 of the edge weight of a maximum weighted matching. Its time complexity is O(|E|), with |E| being the number of edges in the graph. This improves over the previously known 1/2-approximation algorithms for maximum weighted matching which require O(|E| log(|V|)) steps, where |V| is the number of vertices.

. We propose a general methodology for testing whether a given polynomial with integer coefficients is identically zero. The methodology evaluates the polynomial at efficiently computable approximations of suitable irrational points. In contrast to the classical technique of DeMillo, Lipton, Schwartz, and Zippel, this methodology can decrease the error probability by increasing the precision of the approximations instead of using more random bits. Consequently, randomized algorithms that use the classical technique can generally be improved using the new methodology. To demonstrate the methodology, we discuss two nontrivial applications. The first is to decide whether a graph has a perfect matching in parallel. Our new NC algorithm uses fewer random bits while doing less work than the previously best NC algorithm by Chari, Rohatgi, and Srinivasan. The second application is to test the equality of two multisets of integers. Our new algorithm improves upon the previously best algorithms ...

Petersen's theorem is a classic result in matching theory from 1891, stating that every 3-regular bridgeless graph has a perfect matching. Our work explores efficient algorithms for finding perfect matchings in such graphs. Previously, the only relevant matching algorithms were for general graphs, and the fastest algorithm ran in O(n^3/2) time for 3-regular graphs. We have developed an O(n log^4 n)-time algorithm for perfect matching in a 3-regular bridgeless graph. When the graph is also planar, we have as the main result of our paper an optimal O(n)-time algorithm. We present three applications of this result: terrain guarding, adaptive mesh refinement, and quadrangulation.

We present a quantum algorithm for finite domain constraint solving, where the constraints have arity 2. It is complete and runs in O((dd=2e) ) time, where d is size of the domain of the variables and n the number of variables. For the case of d = 3 we provide a method to obtain an upper time bound of O(8 ). Also for d = 5 the upper bound has been improved. Using this method in a slightly different way we can decide 3-colourability in O(1:2185 ) time.

In [2, 3], we have reduced the problem of finding an augmenting path in a general graph to a reachability problem in a directed, bipartite graph, and we have shown that a slight modification of depth-first search leads to an algorithm for finding such paths. This new point of view enables us to give a simplified realization of the Hopcroft-Karp approach for the computation of a maximum cardinality matching in general graphs. We show, how to get an O(n+ m) implementation of one phase leading to an O( p nm) algorithm for the computation of a maximum cardinality matching in general graphs.

Let A and B be two sets of n points in the plane, and let M be a (one-to-one) matching between A and B. Let min(M ), max(M ), and \Sigma(M ) denote the length of the shortest edge, the length of the longest edge, and the sum of the lengths of the edges of M respectively. The uniform matching problem (also called the balanced assignment problem, or the fair matching problem) is to find M U , a matching that minimizes max(M ) \Gamma min(M ). A minimum deviation matching M D is a matching that minimizes (1=n)\Sigma(M ) \Gamma min(M ). We present algorithms for computing M U and M D in roughly O(n 10=3 ) time. These algorithms are more efficient than the previous O(n 4 )-time algorithms of Martello and Toth [19] and Gupta and Punnen [11], who studied these problems for general bipartite graphs. We also consider the (non-bipartite version of the) Euclidean bottleneck matching problem in higher dimensions. We extend the planar results of Chang et al. [4] and Su and Chang [22], and show that given a set A of 2n points in d-space, it is possible to compute a bottleneck matching of A in roughly O(n 3=2 ) time, for d 6, and in subquadratic time, for any fixed dimension d. School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69982, Israel. alone@cs.tau.ac.il y Department of Computer Science, Utrecht University, P.O.Box 80.089, 3508 TB Utrecht, The Netherlands. matya@cs.ruu.nl 0