Related papers: Phase transition in the knapsack problem
Many systems have to be maintained while the underlying constraints, costs and/or profits change over time. Although the state of a system may evolve during time, a non-negligible transition cost is incured for transitioning from one state…
I present an analytic approach to establishing the presence of phase transitions in a large set of decision problems. This approach does not require extensive computational study of the problems considered. The set -- that of all paddable…
Here we present a combinatorial decision problem, inspired by the celebrated quiz show called the countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic…
We discuss how phase-transitions may be detected in computationally hard problems in the context of Anytime Algorithms. Treating the computational time, value and utility functions involved in the search results in analogy with quantities…
While there are various approaches to benchmark physical processors, recent findings have focused on computational phase transitions. This is due to several factors. Importantly, the hardest instances appear to be well-concentrated in a…
Several basic problems of the theory of quantum phase transitions are reviewed. The effect of the quantum correlations on the phase transition properties is considered with the help of basic models of statistical physics. The effect of…
Heuristic methods for solution of problems in the NP-Complete class of decision problems often reach exact solutions, but fail badly at "phase boundaries", across which the decision to be reached changes from almost always having one value…
The stochastic knapsack has been used as a model in wide ranging applications from dynamic resource allocation to admission control in telecommunication. In recent years, a variation of the model has become a basic tool in studying problems…
The problem of distributing the workload on a parallel computer to minimize the overall runtime is known as Multiprocessor Scheduling Problem. It is NP-hard, but like many other NP-hard problems, the average hardness of random instances…
We introduce a prime number generator in the form of a stochastic algorithm. The character of such algorithm gives rise to a continuous phase transition which distinguishes a phase where the algorithm is able to reduce the whole system of…
In the last 30 years it was found that many combinatorial systems undergo phase transitions. One of the most important examples of these can be found among the random k-satisfiability problems (often referred to as k-SAT), asking whether…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
The world is dynamic and changes over time, thus any optimization problem used to model real life problems must address this dynamic nature, taking into account the cost of changes to a solution over time. The multistage model was…
We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase…
We report an analytic and numerical study of a phase transition in a P problem (the assignment problem) that separates two phases whose representatives are the simple matching problem (an easy P problem) and the traveling salesman problem…
Quantum phase transitions encompass a variety of phenomena that occur in quantum systems exhibiting several possible symmetries. Traditionally, these transitions are explored by continuously varying a control parameter that connects two…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
In this paper, we analyze the decision version of the NK landscape model from the perspective of threshold phenomena and phase transitions under two random distributions, the uniform probability model and the fixed ratio model. For the…
We develop a novel mathematical programming approximation framework to tackle the stochastic knapsack problem. In this problem, the decision maker considers items for which either weights or values, or both, are random. The aim is to select…
This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational challenges posed by quantum phase…