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90
Complexity classification of some edge modification problems
, 2001
"... 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 NPhardness of a variety of edge modification problems with respect to some wellstudied classes of graphs. These include perfect, chordal, chain, c ..."
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Cited by 41 (2 self)
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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 NPhardness of a variety of edge modification problems with respect to some wellstudied 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.
On the Complexity of DNA Physical Mapping
, 1994
"... 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 NPcomplete problems, which are conjectured to be computationa ..."
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Cited by 40 (7 self)
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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 NPcomplete 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 Complexity of Querying Indefinite Data about Linearly Ordered Domains
 In The Proceedings of the Eleventh ACM SIGACTSIGMODSIGART Symposium on Principles of Database Systems
, 1992
"... In applications dealing with ordered domains, the available data is frequently indefinite. While the domain is actually linearly ordered, only some of the order relations holding between points in the data are known. Thus, the data provides only a partial order, and query answering involves determin ..."
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Cited by 40 (2 self)
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In applications dealing with ordered domains, the available data is frequently indefinite. While the domain is actually linearly ordered, only some of the order relations holding between points in the data are known. Thus, the data provides only a partial order, and query answering involves determining what holds under all the compatible linear orders. In this paper we study the complexity of evaluating queries in logical databases containing such indefinite information. We show that in this context queries are intractable even under the data complexity measure, but identify a number of PTIME subproblems. Data complexity in the case of monadic predicates is one of these PTIME cases, but for disjunctive queries the proof is nonconstructive, using wellquasiorder techniques. We also show that the query problem we study is equivalent to the problem of containment of conjunctive relational database queries containing inequalities. One of our results implies that the latter is \Pi p 2 ...
Processing Disjunctions in Temporal Constraint Networks
 Artificial Intelligence
, 1997
"... The framework of Temporal constraint Satisfaction Problems (TCSP) has been proposed for representing and processing temporal knowledge. Deciding consistency of TCSPs is known to be intractable. As demonstrates in this paper, even local consistency algorithms like pathconsistency can be exponential ..."
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Cited by 37 (2 self)
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The framework of Temporal constraint Satisfaction Problems (TCSP) has been proposed for representing and processing temporal knowledge. Deciding consistency of TCSPs is known to be intractable. As demonstrates in this paper, even local consistency algorithms like pathconsistency can be exponential due to the fragmentation problem. We present two new polynomial approximation algorithms, UpperLowerTightening (ULT) and LoosePathConsistency (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.
The Meeting Graph: A New Model for Loop Cyclic Register Allocation
 In Proc. of the Fifth Workshop on Compilers for Parallel Computers (CPC95
, 1995
"... 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 registe ..."
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Cited by 31 (11 self)
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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...
A Unifying Approach to Temporal Constraint Reasoning
 Artificial Intelligence
"... 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 ..."
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Cited by 31 (9 self)
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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 polynomialtime satisfiability problem. We prove that most approaches to tractable temporal constraint reasoning can be encoded as Horn DLRs, including the ORDHorn 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...
Reasoning About Temporal Relations: The Tractable Subalgebras Of Allen's Interval Algebra
 Journal of the ACM
, 2001
"... 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 c ..."
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Cited by 31 (2 self)
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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 NPcomplete. 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.
Pathwidth, Bandwidth and Completion Problems to Proper Interval Graphs with Small Cliques
 SIAM Journal on Computing
, 1996
"... 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 kcoloring c of G, does there exist a supergraph We show th ..."
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Cited by 29 (6 self)
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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 kcoloring 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 NPhard, 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.
Twentyone Large Tractable Subclasses of Allen's Algebra
 ARTIFICIAL INTELLIGENCE
, 1997
"... 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 ORDHorn subclass. Furthermore, twelve tractable subclasses are identifi ..."
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Cited by 23 (8 self)
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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 ORDHorn 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 ORDHorn algebra. All of the algebras are considerably larger than the ORDHorn 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.
Eight Maximal Tractable Subclasses of Allen's Algebra with Metric Time
, 1997
"... 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, ..."
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Cited by 22 (10 self)
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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...