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Complexity and approximation: combinatorial optimization problems and their approximability properties

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The Preemptive Uniprocessor Scheduling of Mixed-Criticality Implicit-Deadline Sporadic Task Systems

TLDR
An algorithm called EDF-VD (for Earliest Deadline First with Virtual Deadlines) is described for the scheduling of such mixed-criticality task systems, andalyses of EF-VD significantly superior to previously-known ones are presented, based on metrics such as processor speedup factor and utilization bounds.
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Complexity and Approximation

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Scheduling Real-Time Mixed-Criticality Jobs

TLDR
The intractability of determining whether a system specified in this model can be scheduled to meet all its certification requirements, even for systems subject to merely two sets of certification requirements is demonstrated.
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Multiprocessor scheduling with rejection

TLDR
A version of multiprocessor scheduling with the special feature that jobs may be rejected at a certain penalty is considered, which yields a 1 + 2:618 competitive algorithm for the on-line version of the problem, where is the golden ratio.
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Feasibility Analysis in the Sporadic DAG Task Model

TLDR
This work completely closes the gap between the algorithmic understanding of feasibility analysis for the usual sporadic task model and the case where each sporadic task is a DAG, and presents polynomial and pseudopolynomial time tests for determining whether a set of sporadic DAG tasks can be scheduled by EDF or DM to meet all deadlines on a specified number of processors.
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Response-Time Analysis of Conditional DAG Tasks in Multiprocessor Systems

TLDR
This work integrates control flow information in the task model, considering conditional parallel tasks (cp-tasks) represented by DAGs composed of both precedence and conditional edges, and significantly tightens the schedulability analysis of non-conditional tasks over existing approaches.
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Mixed-Criticality Scheduling of Sporadic Task Systems

TLDR
It is shown that any 2-level task system that is schedulable on a unit-speed processor is correctly scheduled by EDF-VD using speed φ here φ 2 criticality levels, which proves speedup bounds for scheduling an independent collection of jobs and for the partitioned scheduling of a 2- level task system.
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Stochastic on-line knapsack problems

TLDR
A linear time on-line algorithm is proposed for which the expected difference between the optimum and the approximate solution value is O(log3/2n), and anΩ(1) lower bound on the expected Difference between the optimal and the solution found by any on- line algorithm is shown to hold.
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Counting triangles in data streams

TLDR
Two space bounded random sampling algorithms that compute an approximation of the number of triangles in an undirected graph given as a stream of edges are presented and they provide a basic tool to analyze the structure of large graphs.
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