David S. Johnson

• PhD
• Professor at Columbia University

In this paper we consider two special cases of the "cover-by-pairs" optimization problem that arise when we need to place facilities so that each customer is served by two facilities that reach it by disjoint shortest paths. These problems arise in a network traffic monitoring scheme proposed by Breslau et al. and have potential applications to con...

In this paper we consider two special cases of the "cover-by-pairs" optimization problem that arise when we need to place facilities so that each customer is served by two facilities that reach it by disjoint shortest paths. These problems arise in a network traffic monitoring scheme proposed by Breslau et al. and have potential applications to con...

The year 2012 marks the 40th anniversary of the publication of the influential paper “Reducibility among combinatorial problems” by R. M. Karp [in: Complexity of Computer Computations 1972. New York: Plenum Press. 85–103 (1972)]. This paper was the first to demonstrate the wide applicability of the concept now known as NP-completeness, which had be...

This paper is a theoretical and experimental study of two related facility location problems that emanated from networking. Suppose we are given a network modeled as a directed graph G = (V, A), together with (not-necessarily-disjoint) subsets C and F of V, where C is a set of customer locations and F is a set of potential facility locations (and t...

Today's networks typically handle traffic engineering (e.g., tuning the routing-protocol parameters to optimize the flow of traffic) and failure recovery (e.g., pre-installed backup paths) independently. In this paper, we propose a unified way to balance load efficiently under a wide range of failure scenarios. Our architecture supports flexible sp...

Indices for site prioritization are widely used to address the question: which sites are most important for conservation of biodiversity? We investigate the theoretical underpinnings of target-based prioritization, which measures sites’ contribution to achieving predetermined conservation targets. We show a strong connection between site prioritiza...

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1973.

To enable reliable data delivery and balance load in the presence of failures, we propose a new mechanism that combines path protection and traffic engineering. The key benefit of our solution is its simplicity, allowing for fast recovery while imposing minimal requirements on the routers. To provide resilience against every failure scenario from a...

The IMPASSE class of local search algorithms have given good results on many vertex colouring benchmarks. Previous work enhanced IMPASSE by adding the constraint programming technique of forward checking, in order to prune colouration neighbourhoods ...

The purpose of this paper is to provide a preliminary report on the first broad-based experimental comparison of modern heuristics for the asymmetric traveling salesmen problem (ATSP). There are currently three general classes of such heuristics: classical tour construction heuristics such as Nearest Neighbor and the Greedy algorithm, local search...

reviousweaker bounds) actually holds for randomized algorithms against obliviousadversary.On the other hand, the best known deterministic algorithm is the 1:5888competitive HARMONIC+1 by Richey [8] which groups packets by size into morethan 70 categories which are then packed independently. We will see next thata few simple greedy algorithms do not...

Keywords and SynonymsTest sets and experimental evaluation of computer programs for solving shortest path problems; DIMACS Problem DefinitionDIMACS Implementation Challenges (http:// dimacs. rutgers. edu/ Challenges/ ) are scientific events devoted to assessing the practical performance of algorithms in experimental settings, fostering effective te...

Measuring the indirect cost of context switch is a challenging problem. In this paper, we show our results of experimentally quantifying the indirect cost of context switch using a synthetic workload. Specifically, we measure the impact of program data ...

This is the 26th edition of a column,that covers new,developments in the theory of NP-completeness. The presentation is modeled on that which M. R. Garey and I used in our book \Computers and Intractability: A Guide to the Theory of NP-Completeness," W. H. Freeman & Co., New York, 1979, hereinafter referred to as \[G&J]." Previous columns, the rst...

We consider a geometric model for the problem of minimiz- ing access control lists (ACLs) in network routers, a model that also has applications to rectilinear picture compression and figure drawing in common graphics software packages. Here the goal is to create a colored rectilinear pattern within an initially white rectangular canvas, and the ba...

This is the 25th edition of a column,that covers new,developments in the theory of NP-completeness. The presentation is modeled on that which M. R. Garey and I used in our book \Computers and Intractability: A Guide to the Theory of NP-Completeness," W. H. Freeman & Co., New York, 1979, hereinafter referred to as \[G&J]." Previous columns, the rst...

The Sum of Squares algorithm for bin packing was defined in [2] and studied in great detail in [1], where it was proved that its worst case performance ratio is at most 3. In this note, we improve the asymptotic worst case bound to 2.7777...

This is the 24th edition of a column that covers new developments in the theory of NP-completeness. The presentation is modeled on that which M. R. Garey and I used in our book “Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., New York, 1979, hereinafter referred to as “[G&J].” Previous columns, the firs...

We present visibility computation and data organization algorithms that enable high-fidelity walkthroughs of large 3D geometric data sets. A novel feature of our walkthrough system is that it performs work proportional only to the required detail in visible geometry at the rendering time. To accomplish this, we use a precomputation phase that effic...

This chapter describes the way to compress large Boolean matrices using reordering techniques. These matrices are a basic representational unit in a variety of applications, such as interactive visualization systems, mining large graph structures, and association rule mining. Designing space and time efficient scalable storage and query mechanisms...

Large boolean matrices are a basic representational unit in a variety of applications, with some notable examples being interactive visualization systems, mining large graph structures, and association rule mining. Designing space and time e#cient scalable storage and query mechanisms for such large matrices is a challenging problem.

A random method for generated binary trees is presented, ad twp forms of a class of one person games called, "Tree Solitaire" which have such trees as their game trees are defined. After what "look ahead strategy" means in terms of such games is discussed, as theorem on the most efficient use of unlimited look-ahead is proved, and a collection of s...

Today, most large companies maintain virtual private networks (VPNs) to connect their remote locations into a single secure network. VPNs can be quite large covering more than 1000 locations and in most cases use standard Internet protocols and services. Such VPNs are implemented using a diverse set of technologies such as Frame Relay, MPLS, or IPS...

Traceroute is used heavily by network operators and researchers to identify the IP forwarding path from a source to a destination. In practice, knowing the autonomous system (AS) associated with each hop in the path is also quite valuable. In previous work we showed that the IP-to-AS mapping extracted from BGP routing tables is not sufficient for d...

We report on an experimental study of the Gilmore-Gomory cutting-stock heuristic and related LP-based approaches to bin packing, as applied to instances generated according to discrete distributions. No polynomial running time bound is known to hold for the Gilmore-Gomory approach, and empirical operation counts suggest that no straightforward impl...

In this paper we present a theoretical analysis of the deterministic on-line Sum of Squares algorithm (SS) for bin packing introduced and studied experimentally in [CJK 99], along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s(a) are integral (or can be scaled to be so), and r...

In this paper we present a theoretical analysis of the deterministic on-line {\em Sum of Squares} algorithm ($SS$) for bin packing introduced and studied experimentally in \cite{CJK99}, along with several new variants. $SS$ is applicable to any instance of bin packing in which the bin capacity $B$ and item sizes $s(a)$ are integral (or can be scale...

We consider the one-dimensional bin packing problem under the discrete uniform distributions U{j, k}, 1 1, in which the bin capacity is k and item sizes are chosen uniformly from the set 2, . . . , j}. Note that for 0 < u = j/k 1 this is a discrete version of the previously studied continuous uniform distribution U(0, u], where the bin capacity is...

We consider the traveling salesman problem when the cities are points in R^d for some fixed d and distances are computed according to geometric distances, determined by some norm. We show that for any polyhedral norm, the problem of finding a tour of maximum length can be solved in polynomial time. If arithmetic operations are assumed to take unit...

This paper presents an informal discussion of issues that arise when one attempts to an- alyze algorithms experimentally. It is based on lessons learned by the author over the course of more than a decade of experimentation, survey paper writing, refereeing, and lively dis- cussions with other experimentalists. Although written from the perspective...

Introduction In this chapter, we consider what approaches one should take when confronting a real-world application of the asymmetric TSP, that is, the general TSP in which the distance d(c; c 0 ) from city c to city c 0 need not equal the reverse distance d(c 0 ; c). As in the previous chapter on heuristics for the symmetric TSP, we will discuss t...

This paper presents an informal discussion of issues that arise when one attempts to analyze algorithms experimentally. It is based on lessons learned by the author over the course of more than a decade of experimentation, survey paper writing, refereeing, and lively discussions with other experimentalists. Although written from the perspective of...

Introduction In this and the following chapter, we consider what approaches one should take when one is confronted with a real-world application of the TSP. What algorithms should be used under which circumstances? We are in particular interested in the case where instances are too large for optimization to be feasible. Here theoretical results can...

This is for the abstract page Bin Packing with Discrete Item Sizes Part II: Average-Case Behavior of FFD and BFD E. G. Coffman, Jr. and D. S. Johnson AT&T Bell Laboratories Murray Hill, NJ 07974 L. A. McGeoch Amherst College Amherst, MA 01002 R. R. Weber Cambridge University Cambridge UK 1. Introduction Consider the bin packing problem in which a l...

This paper reports on experiments with a new on-line heuristic for one-dimensional bin packing whose average-case behavior is surprisingly robust. We restrict attention to the class of “discrete” distributions, i.e., ones in which the set of possible item sizes is finite (as is commonly the case in practical applications), and in which all sizes an...

Bin covering takes as input a list of item sizes and places them into bins of unit demand so as to maximize the number of bins whose demand is satisfied. This is in a sense a dual problem to the classical one-dimensional bin packing problem, but has for many years lagged behind the latter as far as the quality of the best approximation algorithms....

We consider the one-dimensional bin packing problem with unit-capacity bins and item sizes chosen according to the discrete uniform distribution U{j, k}, 1 < j less than or equal to k, where each item size in {1/k, 2/k,...,j/k} has probability 1/j of being chosen. Note that for fixed j, k as m --> infinity the discrete distributions U{mj, mk} appro...

We consider variants on the Prize Collecting Steiner Tree problem and on the primal-dual 2-approximation algorithm devised for it by Goemans and Williamson. We introduce an improved pruning rule for the algorithm that is slightly faster and provides solutions that are at least as good and typically significantly better. On a selection of real-world...

The last 20 years have seen enormous progress in the design of algorithms, but very little of it has been put into practice, even within academia; indeed, the gap between theory and practice has continuously widened over these years. Moreover, many of the recently developed algorithms are very hard to characterize theoretically and, as initially de...

Branch alignment reorders the basic blocks of a program to minimize pipeline penalties due to controltransfer instructions. Prior work in branch alignment has produced useful heuristic methods. We compute lower bounds on the runtime costs frompipeline penalties and present an intraprocedural branch alignment algorithm that approaches the bound. We...

For this note we say that a problem is computable in time sub-exponential in n if there is an effectively computable monotone increasing function g(n) with lim n→∞ g(n)=∞ such that the problem is computable in time O(2 n/g(n) ). We establish that a maximal independent set of a graph on n vertices can be found in time sub-exponential in n iff the sa...

We consider the traveling salesman problem when the cities are points in Rd for some fixed d and distances are computed according to a polyhedral norm. We show that for any such norm, the problem of finding a tour of maximum length can be solved in polynomial time. If arithmetic operations are assumed to take unit time, our algorithms run in time O...

We consider the traveling salesman problem when the cities are points in IR d for some fixed d and distances are computed according to a polyhedral norm. We show that for any such norm, the problem of finding a tour of maximum length can be solved in polynomial time. If arithmetic operations are assumed to take unit time, our algorithms run in time...

We discuss geometric special cases of optimization problems on graphs where the n vertices are represented as points in IR d and where the lengths of the edges are measured according to a norm with a polyhedral unit ball. We derive algorithms whose running time is polynomial in n (and depends exponentially on the number of faces of the unit ball)....

We study the capacity of cellular systems with interference-adaptation dynamic channel allocation (DCA) through a set of heuristics that evaluate the required number of channels for some mobile traffic pattern. In particular, we evaluate the improvement in the reuse factor given the knowledge of the mobiles' locations. Assuming that the mobiles' lo...

This report focuses oll two core areas of theory of computing: discrete algorithms and computational complexity theory. The report reviews the purposes and goals of theoretical research, summarizes selected past and recent achievements, explains the importance of sustaining core research, and identifies promising opportunities for filture research....

In the bin packing problem, a list L of n items is to be packed into a sequence of unit capacity bins with the goal of minimizing the number of bins used. First Fit (FF) is one of the most natural on-line algorithms for this problem, based on the simple rule that each successive item is packed into the first bin of the sequence that currently has r...

This is a preliminary version of a chapter that appeared in the book Local Search in Combinatorial Optimization, E. H. L. Aarts and J. K. Lenstra (eds.), John Wiley and Sons, London, 1997, pp. 215-310. The traveling salesman problem (TSP) has been an early proving ground for many approaches to combinatorial optimization, including clas- sical local...

In the bin packing problem, a list L of n items is to be packed into a sequence of unit capacity bins with the goal of minimizing the number of bins used. First Fit (FF) is one of the most natural on-line algorithms for this problem, based on the simple rule that each successive item is packed into the first bin of the sequence that currently has r...

The principles underlying this report can be summarized as follows: 1. A strong theoretical foundation is vital to computer science. 2. Theory can be enriched by practice. 3. Practice can be enriched by theory. 4. If we consider (2) and (3), the value, impact, and funding of theory will be enhanced. In order to achieve a greater synergy between the...

As you probably already know, there is an active discussion going on---in forums ranging from lunch-table conversations to workshops on "strategic directions" to formal reports---regarding the future of theoretical computer science. Since your complexity ...

The Web directory of Computational Geometry Software is described.

The Held-Karp (HK) lower bound is the solution to the linear pro- gramming relaxation of the standard integer programming formu- lation of the traveling salesman problem (TSP). For numbers of cities N up to 30,000 or more it can be computed exactly using the Simplex method and appropriate separation algorithms, and for N up to a million good approx...

The Held-Karp (HK) lower bound is the solution to the linear programming relaxation of the standard integer programming formulation of the traveling salesman problem (TSP). For numbers of cities N up to 30,000 or more it can be computed exactly using the Simplex method and appropriate separation algorithms, and for N up to a million good approximat...

We investigate the capacity of cellular systems. In particular, we study how the reuse factor can be improved given the knowledge of the mobiles' locations; i.e., we evaluate the minimum number of channels required to support a cellular infrastructure with a given number of mobiles in each cell. We assume that the mobiles' locations are sampled fro...

In the Multiterminal Cut problem we are given an edge-weighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the min- cut, max-flow problem, and can be solved in polynomial time. We show that the...

An abstract is not available.

The paper describes the overall conclusions from the evaluation of the traveling salesman problem. Also discussed are the algorithms and the undominated heuristics used. The authors show approaches like simulated annealing, tabu search, genetic algorithms and neural nets being used in the evaluation of the problem.

In this paper, we extend our previously published results on the capacity of cellular systems to include the effects of shadow fading and power control. These studies investigate how the reuse factor can be improved given the knowledge of mobiles' locations. We use square-root power control, which we prove is the optimal power control strategy

In the last 10 years, there have been major advances in the average-case analysis of bin packing, scheduling and similar partitioning problems in one and two dimensions. These problems are drawn from important applications throughout industry, often under the name of stock cutting. This article briefly surveys many of the basic results, as well as...

The choice of data structure for tour representation plays a critical role in the efficiency of local improvement heuristics for the Traveling Salesman Problem. The tour data structure must permit queries about the relative order of cities in the current tour and must allow sections of the tour to be reversed. The traditional array-based representa...

An abstract is not available.

In the Multiway Cut problem we are given an edge-weighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the min-cut, max-flow problem, and can be solved in polynomial time. We show that the probl...

This is the second in a series of three papers that empirically examine the competitiveness of simulated annealing in certain well-studied domains of combinatorial optimization. Simulated annealing is a randomized technique proposed by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi for improving local optimization algorithms. Here we report on exper...

We present a sequence of new linear-time, bounded-space, on-line bin packing algorithms, the K -Bounded Best Fit algorithms (BBFK ). They are based on the Θ(n log n) Best Fit algorithm in much the same way as the Next-K Fit algorithms are based on the Θ(n log n) First Fit algorithm. Unlike the Next-K Fit algorithms, whose asymptotic worst-case rati...

This chapter discusses the concepts needed for defining the complexity classes. A complexity class is a set of problems of related resource-based complexity. A typical complexity class has a definition of the form—the set of problems that can be solved by an abstract machine M using O(f(n)) of resource R, where n is the size of the input. The simpl...

An abstract is not available.

Unit disk graphs are the intersection graphs of equal sized circles in the plane: they provide a graph-theoretic model for broadcast networks (cellular networks) and for some problems in computational geometry. We show that many standard graph theoretic problems remain NP-complete on unit disk graphs, including coloring, independent set, domination...

Unit disk graphs are the intersection graphs of equal sized circles in the plane: they provide a graph-theoretic model for broadcast networks (cellular networks) and for some problems in computational geometry. We show that many standard graph theoretic problems remain NP-complete on unit disk graphs, including coloring, independent set, domination...

The Traveling Salesman Problem (TSP) is often cited as the prototypical hard combinatorial optimization problem. As such, it would seem to be an ideal candidate for nonstandard algorithmic approaches, such as simulated annealing, and, more recently, genetic algorithms. Both of these approaches can be viewed as variants on the traditional technique...

In this paper, we prove that maximum planar H-matching (the problem of determining the maximum number of node-disjoint copies of the fixed graph H contained in a variable planar graph G) is NP-complete for any connected planar graph H with three or more nodes. We also show that perfect planar H-matching is NP-complete for any connected outerplanar...

This is the 23rd edition of an irregularly appearing column that covers new developments in the theory of NP-completeness. 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 NP-Completeness," W. H. Freeman & Co., New York, 1979 (hereinafter referred to as "[G&J]"; p...

Without Abstract