The dynamic version of the maximum flow problem allows the graph underlying the flow network to change over time. The graph receives corrections to its structure or capacities and consequently the value of the maximum flow is modified. These corrections arrive in real time. In this paper, parallel and sequential solutions to the real-time maximum flow problem are developed on the Reconfigurable Multiple Bus Machine (RMBM) model and on the Random Access Machine (RAM) model, respectively. The parallel solution successfully meets the deadlines imposed in real time, while the sequential one fails to do so. The two solutions are then applied to a real-time process scheduler, an extension of Stone's static twoprocessor allocation problem. The scheduler allows processes to be created and destroyed, the amount of communication between two processes to change with time, and so on. The parallel algorithm is always able to compute the optimal schedule, while the solution obtained sequentially is only an approximation. The improvement provided by the parallel approach over the sequential one is superlinear in the number of processors used by the parallel model. Key words and phrases: maximum flow, parallelism, real-time computation, module allocation. 1

A general framework is proposed for the study of real-time algorithms. The framework unifies previous algorithmic definitions of real-time computation. In it, state space traversal is used as a model for computational problems in a real-time environment. The proposed framework also employs a paradigm, known as discrete steepest descent, for algorithms designed to solve these problems. Sequential and parallel algorithms for traversing a state space by discrete steepest descent are then analyzed and compared. The analysis measures the value (or worth) of a computed solution. The quantity used in the evaluation may be the time required by an algorithm to reach the solution, the quality of the solution obtained, or any similar measure. The value of a real-time solution obtained in parallel is shown to be consistently superior to that of a solution computed sequentially by an amount superlinear in the size of the problem.

Determining the optimal location of a switching center in a tree network of users is accurately modeled by the median problem. A real-time approach is used in this paper to investigate the dynamics of such a communication network in two cases: (1) a growing tree of nodes associated with equal demand rates, and (2) a stream of corrections that arbitrarily change the demand rates at the nodes. The worst-case analysis performed in both situations clearly demonstrates the importance of parallelism in such real-time paradigms. It is shown that the error generated by the best sequential algorithm in the first case can be arbitrarily large. A synergistic behavior is revealed when the quality-up is investigated in the second case. 1

It is shown that the concept of a Universal Computer cannot be realized. Specifically, instances of a computable function F are exhibited that cannot be computed on any machine U that is capable of only a finite and fixed number of operations per step. This remains true even if the machine U is endowed with an infinite memory and the ability to communicate with the outside world while it is attempting to compute F. It also remains true if, in addition, U is given an indefinite amount of time to compute F. This result applies not only to idealized models of computation, such as the Turing Machine and the like, but also to all known general-purpose computers, including existing conventional computers, as well as contemplated ones such as quantum computers.

Abstract—We describe QoSMap, an overlay construction mechanism which computes high quality overlay networks for applications having stringent constraints on hop-degrading QoS metrics and provides resilience against the Internet’s unpredictable network behavior. QoSMap implements three features to achieve the QoS and resiliency goals. In order to provide high QoS, it constructs overlay communication edges with short but efficient underlay paths. In case of QoS violations due to changing network conditions, QoSMap utilizes supplemental backup paths, which are specifically constructed in order to extend overlay lifetimes. QoSMap also avoids nodes that have experienced recent QoS failure, further improving the resilience of the overlays. PlanetLab experiments prove the ability of QoSMap to construct efficient and resilient overlays for applications with stringent QoS constraints of latency and packet loss for a variety of topologies. QoSMap-constructed overlays significantly outperform overlays constructed without the three QoSMap features. The results also reveal the usability and effectiveness of QoSMap to construct near-optimal solution in a short amount of time, compared to the optimal solution which has a very high time complexity.

A new computational paradigm is described which offers the possibility of superlinear (and sometimes unbounded) speedup, when parallel computation is used. The computations involved are subject only to given mathematical constraints and hence do not depend on external circumstances to achieve superlinear performance. The focus here is on geometric transformations. Given a geometric object A with some property, it is required to transform A into another object B which enjoys the same property. If the transformation requires several steps, each resulting in an intermediate object, then each of these intermediate objects must also obey the same property. We show that in transforming one triangulation of a polygon into another, a parallel algorithm achieves a superlinear speedup. In the case where a convex decomposition of a set of points is to be transformed, the improvement in performance is unbounded, meaning that a parallel algorithm succeeds in solving the problem as posed, while all sequential algorithms fail.