Results 11  20
of
1,499
The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & ..."
Abstract

Cited by 190 (0 self)
 Add to MetaCart
This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Multicast Routing for Multimedia Communication
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1993
"... We present heuristics for multicast tree construction for communication that depends on: i) bounded endtoend delay along the paths from source to each destination, and ii) minimum cost of the multicast tree, where edge cost and edge delay can be independent metrics. This problem of computing such ..."
Abstract

Cited by 190 (9 self)
 Add to MetaCart
We present heuristics for multicast tree construction for communication that depends on: i) bounded endtoend delay along the paths from source to each destination, and ii) minimum cost of the multicast tree, where edge cost and edge delay can be independent metrics. This problem of computing such a constrained multicast tree is NPcomplete. We show that the heuristics demonstrate good average case behavior in terms of cost, as determined through simulations on a large number of graphs.
Truth revelation in approximately efficient combinatorial auctions
 Journal of the ACM
, 2002
"... Abstract. Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a difficult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard ..."
Abstract

Cited by 187 (1 self)
 Add to MetaCart
Abstract. Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a difficult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard for combinatorial auctions, the Generalized Vickrey Auction (GVA). Traditional analysis of these mechanisms—in particular, their truth revelation properties—assumes that the optimization problems are solved precisely. In reality, these optimization problems can usually be solved only in an approximate fashion. We investigate the impact on such mechanisms of replacing exact solutions by approximate ones. Specifically, we look at a particular greedy optimization method. We show that the GVA payment scheme does not provide for a truth revealing mechanism. We introduce another scheme that does guarantee truthfulness for a restricted class of players. We demonstrate the latter property by identifying natural properties for combinatorial auctions and showing that, for our restricted class of players, they imply that truthful strategies are dominant. Those properties have applicability beyond the specific auction studied.
Algorithms and Complexity Concerning the Preemptive Scheduling of Periodic, RealTime Tasks on One Processor
 RealTime Systems
, 1990
"... We investigate the preemptive scheduling of periodic, realtime task systems on one processor. First, we show that when all parameters to the system are integers, we may assume without loss of generality that all preemptions occur at integer time values. We then assume, for the remainder of the pape ..."
Abstract

Cited by 186 (13 self)
 Add to MetaCart
We investigate the preemptive scheduling of periodic, realtime task systems on one processor. First, we show that when all parameters to the system are integers, we may assume without loss of generality that all preemptions occur at integer time values. We then assume, for the remainder of the paper, that all parameters are indeed integers. We then give as our main lemma both necessary and sufficient conditions for a task system to be feasible on one processor. Although these conditions cannot, in general, be tested efficiently (unless P = NP), they do allow us to give efficient algorithms for deciding feasibility on one processor for certain types of periodic task systems. For example, we give a pseudopolynomial time algorithm for synchronous systems whose densities are bounded by a fixed constant less than 1. This algorithm represents an exponential improvement over the previous best algorithm. We also give a polynomialtime algorithm for systems having a fixed number of distinct typ...
Optimal inapproximability results for MAXCUT and other 2variable CSPs?
, 2005
"... In this paper we show a reduction from the Unique Games problem to the problem of approximating MAXCUT to within a factor of ffGW + ffl, for all ffl> 0; here ffGW ss.878567 denotes the approximation ratio achieved by the GoemansWilliamson algorithm [25]. This implies that if the Unique Games ..."
Abstract

Cited by 178 (28 self)
 Add to MetaCart
In this paper we show a reduction from the Unique Games problem to the problem of approximating MAXCUT to within a factor of ffGW + ffl, for all ffl> 0; here ffGW ss.878567 denotes the approximation ratio achieved by the GoemansWilliamson algorithm [25]. This implies that if the Unique Games
Zero Knowledge and the Chromatic Number
 Journal of Computer and System Sciences
, 1996
"... We present a new technique, inspired by zeroknowledge proof systems, for proving lower bounds on approximating the chromatic number of a graph. To illustrate this technique we present simple reductions from max3coloring and max3sat, showing that it is hard to approximate the chromatic number wi ..."
Abstract

Cited by 178 (8 self)
 Add to MetaCart
We present a new technique, inspired by zeroknowledge proof systems, for proving lower bounds on approximating the chromatic number of a graph. To illustrate this technique we present simple reductions from max3coloring and max3sat, showing that it is hard to approximate the chromatic number within \Omega\Gamma N ffi ), for some ffi ? 0. We then apply our technique in conjunction with the probabilistically checkable proofs of Hastad, and show that it is hard to approximate the chromatic number to within\Omega\Gamma N 1\Gammaffl ) for any ffl ? 0, assuming NP 6` ZPP. Here, ZPP denotes the class of languages decidable by a random expected polynomialtime algorithm that makes no errors. Our result matches (up to low order terms) the known gap for approximating the size of the largest independent set. Previous O(N ffi ) gaps for approximating the chromatic number (such as those by Lund and Yannakakis, and by Furer) did not match the gap for independent set, and do not extend...
Aggregating inconsistent information: ranking and clustering
, 2005
"... We address optimization problems in which we are given contradictory pieces of input information and the goal is to find a globally consistent solution that minimizes the extent of disagreement with the respective inputs. Specifically, the problems we address are rank aggregation, the feedback arc s ..."
Abstract

Cited by 158 (9 self)
 Add to MetaCart
We address optimization problems in which we are given contradictory pieces of input information and the goal is to find a globally consistent solution that minimizes the extent of disagreement with the respective inputs. Specifically, the problems we address are rank aggregation, the feedback arc set problem on tournaments, and correlation and consensus clustering. We show that for all these problems (and various weighted versions of them), we can obtain improved approximation factors using essentially the same remarkably simple algorithm. Additionally, we almost settle a longstanding conjecture of BangJensen and Thomassen and show that unless NP⊆BPP, there is no polynomial time algorithm for the problem of minimum feedback arc set in tournaments. 1
Interactive proofs and the hardness of approximating cliques
 Journal of the ACM
, 1996
"... The contribution of this paper is twofold. First, a connection is shown between approximating the size of the largest clique in a graph and multiprover interactive proofs. Second, an efficient multiprover interactive proof for NP languages is constructed, where the verifier uses very few random b ..."
Abstract

Cited by 157 (11 self)
 Add to MetaCart
The contribution of this paper is twofold. First, a connection is shown between approximating the size of the largest clique in a graph and multiprover interactive proofs. Second, an efficient multiprover interactive proof for NP languages is constructed, where the verifier uses very few random bits and communication bits. Last, the connection between cliques and efficient multiprover interactive proofs, is shown to yield hardness results on the complexity of approximating the size of the largest clique in a graph. Of independent interest is our proof of correctness for the multilinearity test of functions. 1
The Hardness of Approximate Optima in Lattices, Codes, and Systems of Linear Equations
, 1993
"... We prove the following about the Nearest Lattice Vector Problem (in any `p norm), the Nearest Codeword Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor is NPhard. 2. If for some ..."
Abstract

Cited by 154 (7 self)
 Add to MetaCart
We prove the following about the Nearest Lattice Vector Problem (in any `p norm), the Nearest Codeword Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor is NPhard. 2. If for some ffl ? 0 there exists a polynomialtime algorithm that approximates the optimum within a factor of 2 log 0:5\Gammaffl n , then every NP language can be decided in quasipolynomial deterministic time, i.e., NP ` DTIME(n poly(log n) ). Moreover, we show that result 2 also holds for the Shortest Lattice Vector Problem in the `1 norm. Also, for some of these problems we can prove the same result as above, but for a larger factor such as 2 log 1\Gammaffl n or n ffl . Improving the factor 2 log 0:5\Gammaffl n to p dimension for either of the lattice problems would imply the hardness of the Shortest Vector Problem in `2 norm; an old open problem. Our proofs use reductions from fewpr...