An exact algorithm for the subset sum problem

Soma, Nei Yoshihiro; Toth, Paolo

doi:10.1016/s0377-2217(00)00329-5

Cited by 21 publications

(12 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• Problems somatoth: These instances are due to Soma and Toth [441]. First, two weights w' and w" are selected randomly in [1,n), such that gcd(w' , w") = 1 and such that l7 < ~ and ;;r < ~.…”

Section: Computational Results: Exact Algorithmsmentioning

confidence: 99%

See 1 more Smart Citation

Knapsack Problems

2004

View full text Add to dashboard Cite

PrefaceThirteen years have passed since the seminal book on knapsack problems by Martello and Toth appeared. On this occasion a former colleague exclaimed back in 1990: "How can you write 250 pages on the knapsack problem?" Indeed, the definition of the knapsack problem is easily understood even by a non-expert who will not suspect the presence of challenging research topics in this area at the first glance.However, in the last decade a large number of research publications contributed new results for the knapsack problem in all areas of interest such as exact algorithms, heuristics and approximation schemes. Moreover, the extension of the knapsack problem to higher dimensions both in the number of constraints and in the number of knapsacks, as well as the modification of the problem structure concerning the available item set and the objective function, leads to a number of interesting variations of practical relevance which were the subject of intensive research during the last few years.Hence, two years ago the idea arose to produce a new monograph covering not only the most recent developments of the standard knapsack problem, but also giving a comprehensive treatment of the whole knapsack family including the siblings such as the subset sum problem and the bounded and unbounded knapsack problem, and also more distant relatives such as multidimensional, multiple, multiple-choice and quadratic knapsack problems in dedicated chapters.Furthermore, attention is paid to a number of less frequently considered variants of the knapsack problem and to the study of stochastic aspects of the problem. To illustrate the high practical relevance of the knapsack family for many industrial and economic problems, a number of applications are described in more detail. They are selected subjectively from the innumerable occurrences of knapsack problems reported in the literature.Our above-mentioned colleague will be surprised to notice that even on the more than 500 pages of this book not all relevant topics could be treated in equal depth but decisions had to be made on where to go into details of constructions and proofs and where to concentrate on stating results and refer to the appropriate publications. Moreover, an editorial deadline had to be drawn at some point. In our case, we stopped looking for new publications at the end of June 2003. VI PrefaceThe audience we envision for this book is threefold: The first two chapters offer a very basic introduction to the knapsack problem and the main algorithmic concepts to derive optimal and approximate solution. Chapter 3 presents a number of advanced algorithmic techniques which are used throughout the later chapters of the book. The style of presentation in these three chapters is kept rather simple and assumes only minimal prerequisites. They should be accessible to students and graduates of business administration, economics and engineering as well as practitioners with little knowledge of algorithms and optimization.This first part of the book is also well suited to introd...

show abstract

Section: Computational Results: Exact Algorithmsmentioning

confidence: 99%

“…Soma and Toth [441] presented a dynamic programming algorithm, called STOO, which combines Horowitz and Sahni decomposition for a small core with the Bellman recursion in decision form (4.24).…”

Section: Fixed Size Core and Decompositionmentioning

confidence: 99%

Knapsack Problems

2004

View full text Add to dashboard Cite

show abstract

“…Soma and Toth [27] showed that the partition problem can be solved in O(max{(n − 2 log wsum)wsum, wsum log wsum}) time, where wsum = 1 j n wj. We write this algorithm as Algorithm 1.…”

Section: Complexity and Computing Resultsmentioning

confidence: 99%

Coalition formation in weighted simple-majority games under proportional payoff allocation rules

Cao

Yang

2009

Int. J. Autom. Comput.

View full text Add to dashboard Cite

In this paper, we introduce a simple coalition formation game in the environment of bidding, which is a special case of the weighted majority game (WMG), and is named the weighted simple-majority game (WSMG). In WSMG, payoff is allocated to the winners proportional to the players powers, which can be measured in various ways. We define a new kind of stability: the counteraction-stability (C-stability), where any potential deviating players will confront counteractions of the other players. We show that C-stable coalition structures in WSMG always contains a minimal winning coalition of minimum total power. For the variant where powers are measured directly by their weights, we show that it is NP-hard to find a C-stable coalition structure and design a pseudo-polynomial time algorithm. Sensitivity analysis for this variant, which shows many interesting properties, is also done. We also prove that it is NP-hard to compute the Holler-Packel indices in WSMGs, and hence in WMGs as well.

show abstract

“…Phases Soma and Toth [17] conceived a algorithm for the SSP, which combines the dynamic programming and the two-list paradigms. In short, it has four main phases:…”

Section: Phases (I) (Ii) and (Iii) Spent Time O(c/n) O(1)mentioning

confidence: 99%

“…[10], pp. 90-91) introduced an algorithm to sequentially solve the problem in O(n(c − 2w min ) + c) time and space O(n + c); Soma and Toth [17] gave a sequential algorithm which combines dynamic programming and the two-list enumeration to obtain a time complexity of O((n − log c 2 )(c − 2w min ) + c + n) and space O(n + c). Both algorithms configure an improvement in terms of computational resources related to Bellman's approach, and, to the present, no study was carried out on their parallelizations.…”

Section: Introductionmentioning

confidence: 99%

Parallel time and space upper-bounds for the subset-sum problem

Sanches

Soma

Yanasse

2008

Theoretical Computer Science

View full text Add to dashboard Cite

a b s t r a c tThree new parallel scalable algorithms for solving the Subset-Sum Problem in O( n p (c − w min )) time and O(n + c) space in the PRAM model are presented, where n is the number of objects, c is the capacity, w min is the smallest weight and p is the number of processors. These time and space bounds are better than the direct parallelization of Bellman's algorithm, which was the most efficient known result.

show abstract

An exact algorithm for the subset sum problem

Cited by 21 publications

References 7 publications

Knapsack Problems

Knapsack Problems

Coalition formation in weighted simple-majority games under proportional payoff allocation rules

Parallel time and space upper-bounds for the subset-sum problem

Contact Info

Product

Resources

About