منابع مشابه
The Subset Sum game☆
In this work we address a game theoretic variant of the Subset Sum problem, in which two decision makers (agents/players) compete for the usage of a common resource represented by a knapsack capacity. Each agent owns a set of integer weighted items and wants to maximize the total weight of its own items included in the knapsack. The solution is built as follows: Each agent, in turn, selects one...
متن کاملOn a Stackelberg Subset Sum Game
This contribution deals with a two-level discrete decision problem, a so-called Stackelberg strategic game: A Subset Sum setting is addressed with a set $N$ of items with given integer weights. One distinguished player, the leader, may alter the weights of the items in a given subset $L\subset N$, and a second player, the follower, selects a solution $A\subseteq N$ in order to utilize a bounded...
متن کاملMultidimensional Subset Sum Problem
This thesis explores new modifications to the successful LLL approach to solving the Subset Sum problem. This work is an optimization of the matrix representation of an instance. Traditionally, the basis matrix contained only one column with set elements and the sum. In this thesis we suggest having several data columns (thus introducing multidimensionality). This allows us to reduce the size o...
متن کاملSolving the Subset Sum Problem with Heap-Ordered Subset Trees
In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force approach of verifying all combinations of integers, several solutions have been found, ranging from clever uses of various data structures to computationally...
متن کاملSolving Low - density Subset Sum
Definition 1. Subset sum (SSUM) is the following problem: given a1, . . . , an ∈ [0, X] and s = ∑ aixi where each xi ∈ {0, 1}, find ~x = (x1, . . . , xn). Definition 2. The density of a subset sum problem is defined as n logX ; the ratio between the number of elements in your sum to the number of bits in the range of ais. Low density means n logX is very small, for example 1 n2 where X = 2 n . ...
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ژورنال
عنوان ژورنال: European Journal of Operational Research
سال: 2014
ISSN: 0377-2217
DOI: 10.1016/j.ejor.2013.08.047