The theoretical properties of qualitative spatial reasoning in the RCC-8 framework have been analyzed extensively. However, no empirical investigation has been made yet. Our experiments show that the adaption of the algorithms used for qualitative temporal reasoning can solve large RCC-8 instances, even if they are in the phase transition region -- provided that one uses the maximal tractable subsets of RCC-8 that have been identified by us. In particular, we demonstrate that the orthogonal combination of heuristic methods is successful in solving almost all apparently hard instances in the phase transition region up to a certain size in reasonable time.

The Physical Mapping Problem is to reconstruct the relative position of fragments (clones) of DNA along the genome from information on their pairwise overlaps. We show that two simplified versions of the problem belong to the class of NP-complete problems, which are conjectured to be computationally intractable. In one version all clones have equal length, and in another, clone lengths may be arbitrary. The proof uses tools from graph theory and complexity.

The framework of Temporal constraint Satisfaction Problems (TCSP) has been proposed for representing and processing temporal knowledge. Deciding consistency of TC-SPs is known to be intractable. As demonstrates in this paper, even local consistency algorithms like path-consistency can be exponential due to the fragmentation problem. We present two new polynomial approximation algorithms, Upper-Lower-Tightening (ULT) and Loose-Path-Consistency (LPC), which are e cient yet e ective in detecting inconsistencies and reducing fragmentation. The experiments we performed on hard problems in the transition region show that LPC is the superior algorithm. When incorporated within backtrack search LPC is capable of improving performance by orders of magnitude.

In an edge modification problem one has to change the edge set of a given graph as little as possible so as to satisfy a certain property. We prove the NP-hardness of a variety of edge modification problems with respect to some well-studied classes of graphs. These include perfect, chordal, chain, comparability, split and asteroidal triple free. We show that some of these problems become polynomial when the input graph has bounded degree. We also give a general constant factor approximation algorithm for deletion and editing problems on bounded degree graphs with respect to properties that can be characterized by a finite set of forbidden induced subgraphs.

Register allocation is a compiler phase in which the gains can be essential in achieving performance on new architectures exploiting instruction level parallelism. We focus our attention on loops and improve the existing methods by introducing a new kind of graph. We model loop unrolling and register allocation together in a common framework, called the meeting graph. We expect our results to significantly improve loop register allocation while keeping the amount of code replication low. As a byproduct, we present an optimal algorithm for allocating loop variables to a rotating register file, as well as a new heuristic for loop variables spilling. 1 Introduction The efficiency of register allocation is a crucial problem in modern microprocessors, where the increasing gap between the internal clock cycle and memory latency exacerbates the need to keep the variables in registers and to avoid spill code. In this paper, we address the important problem of loop register allocation and spi...

We present a formalism, Disjunctive Linear Relations (DLRs), for reasoning about temporal constraints. DLRs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive. We also present a restricted type of DLRs, Horn DLRs, which have a polynomial-time satisfiability problem. We prove that most approaches to tractable temporal constraint reasoning can be encoded as Horn DLRs, including the ORD-Horn algebra by Nebel and Burckert and the simple temporal constraints by Dechter et al. Thus, DLRs is a suitable unifying formalism for reasoning about temporal constraints. 1 Introduction Reasoning about temporal knowledge abounds in artificial intelligence applications and other areas, such as planning [4], natural language understanding [25] and molecular biology [6, 13]. In most applications, knowledge of temporal constraints is expressed in terms of collections of relations between time intervals or time po...

We study two related problems motivated by molecular biology: ffl Given a graph G and a constant k, does there exist a supergraph G of G which is a unit interval graph and has clique size at most k? ffl Given a graph G and a proper k-coloring c of G, does there exist a supergraph We show that those problems are polynomial for fixed k. On the other hand we prove that the first problem is equivalent to deciding if the bandwidth of G is at most k \Gamma 1. Hence, it is NP-hard, and W [t]-hard for all t. We also show that the second problem is W [1]-hard. This implies that for fixed k, both of the problems are unlikely to have an O(n ) algorithm, where ff is a constant independent of k.

This paper combines two important directions of research in temporal resoning: that of finding maximal tractable subclasses of Allen's interval algebra, and that of reasoning with metric temporal information. Eight new maximal tractable subclasses of Allen's interval algebra are presented, some of them subsuming previously reported tractable algebras. The algebras allow for metric temporal constraints on interval starting or ending points, using the recent framework of Horn DLRs. Two of the algebras can express the notion of sequentiality between intervals, being the first such algebras admitting both qualitative and metric time. 91 1 Introduction Reasoning about temporal knowledge abounds in artificial intelligence applications and other areas, such as planning [ Allen, 1991 ] , natural language understanding [ Song and Cohen, 1988 ] and molecular biology [ Benzer, 1959; Golumbic and Shamir, 1993 ] . However, since even the restricted problem of reasoning with pure qualitative ti...

This paper continues Nebel and Burckert's investigation of Allen's interval algebra by presenting nine more maximal tractable subclasses of the algebra (provided that P != NP), in addition to their previously reported ORD-Horn subclass. Furthermore, twelve tractable subclasses are identified, whose maximality is not decided. Four of them can express the notion of sequentiality between intervals, which is not possible in the ORD-Horn algebra. All of the algebras are considerably larger than the ORD-Horn subclass. The satisfiability algorithm, which is common for all the algebras, is shown to be linear. Furthermore, the path consistency algorithm is shown to decide satisfiability of interval networks using any of the algebras.

Allen's interval algebra is one of the best established formalisms for temporal reasoning. This paper is the final step in the classification of complexity in Allen's algebra. We show that the current knowledge about tractability in the interval algebra is complete, that is, this algebra contains exactly eighteen maximal tractable subalgebras, and reasoning in any fragment not entirely contained in one of these subalgebras is NP-complete. We obtain this result by giving a new uniform description of the known maximal tractable subalgebras and then systematically using an algebraic technique for identifying maximal subalgebras with a given property.