Average-case complexity

About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.

A Reduced-Complexity Tree Search Detection Algorithm for MIMO Systems

Abstract: In this correspondence, we propose a simplified QR-decomposition-M algorithm for coded multiple-input multiple-output systems based on the idea of selective branch extension. The proposed algorithm results in significant complexity reductions without observable performance losses, especially for large modulation orders where complexity reduction is most important.

On the Relative Complexity of 15 Problems Related to 0/1-Integer Programming

Abstract: An integral part of combinatorial optimization and computational complexity consists of establishing relationships between different problems or different versions of the same problem. In this chapter, we bring together known and new, previously published and unpublished results, which establish that 15 problems related to optimizing a linear function over a 0/1-polytope are polynomial-time equivalent. This list of problems includes optimization and augmentation, testing optimality and primal separation, sensitivity analysis and inverse optimization, as well as several others.

Time Complexity and Learning

Abstract: The debate about the physical existence of time1–3 suggests the possibility that time could also be considered an intellectual construction in order to “treat” (that is, to describe/order/analyze) the flux of external events; in addition, it raises the problem of intellectual constructions suitable for “treating” the flux of internal events. On this point, we can speak about “mind times,” metaphors that may help in “treating” mental processes, especially those intervening in complex problem solving. Bearing in mind our competencies (cognitive and epistemological aspects of teaching and learning mathematics), we will consider in a phenomenological manner the variety of “times” that the mind must manage in mathematical problem solving. We will also consider the intertwining among them, mentioning some examples4,5 in which success or failure seems to depend on the capacity to manage such time complexity. Finally, we will consider the hypothesis that the analysis of “mind times” may be useful (in an “embodied cognition” perspective) for singling out some mental processes on which basic mathematical ideas and skills are founded.

On The Complexity of Counter Reachability Games

Abstract: Counter reachability games are played by two players on a graph with labelled edges. Each move consists in picking an edge from the current location and adding its label to a counter vector. The objective is to reach a given counter value in a given location. We distinguish three semantics for counter reachability games, according to what happens when a counter value would become negative: the edge is either disabled, or enabled but the counter value becomes zero, or enabled. We consider the problem of deciding the winner in counter reachability games and show that, in most cases, it has the same complexity under all semantics. Surprisingly, under one semantics, the complexity in dimension one depends on whether the objective value is zero or any other integer.

The Computational Complexity of Linear PCGSs

Abstract: The computational complexity is investigated for Parallel Communicating Grammar Systems (PCGSs) whose components are linear grammars. It is shown that language generated by linear PCGSs can be recognized by O(log n) space/bounded Turing machines. Based on the complexity characterization, the generative power of linear PCGSs is analyzed with respect to context-free and context-sensitive grammars.