This is a survey on an analogue of tropical convexity developed over the max-min semiring, starting with the descriptions of max-min segments, semispaces, hyperplanes and an account of separation and non-separation results based on semispaces. There are some new results. In particular, we give new “colorful” extensions of the max-min Carathéodory theorem. In the end of the paper, we list some c...

We denote as QoS-max the control of a request processing system to try to maximize QoS qualities and we focus on external, non-intrusive approaches with statistics on readily measurable quantities. In order to do this, the controller characterizes requests in terms of response times (or resource use) and uses that characterization to try to achieve QoS-max. However, measures vary both between d...

This paper describes an algorithm that computes the maxmin fair allocation of rates for flows through an input-queued switch. The algorithm is provably max-min fair and can be implemented in a distributed fashion to dynamically determine flow rates.

We generalize a smoothing algorithm for finite min–max to finite min– max–min problems. We apply a smoothing technique twice, once to eliminate the inner min operator and once to eliminate the max operator. In mini–max problems, where only the max operator is eliminated, the approximation function is decreasing with respect to the smoothing parameter. Such a property is convenient to establish ...

The suffix tree is an extremely important data structure in bioinformatics. Classical implementations require much space, which renders them useless to handle large sequence collections. Recent research has obtained various compressed representations for suffix trees, with widely different space-time tradeoffs. In this paper we show how the use of range min-max trees yields novel representation...

This paper considers the main positions of one-sided and two-sided problems. For onesided problems only the method of solution “the distance to the ideal point” is discussed in the actual version. For two-sided problems a distinction is made between games with rational behaviour and games against nature. The main strategic principles are as follows: simple min-max principle, extended min-max pr...

We study on the minimal hedging risk for a bounded European contingent claim when we use a convex risk measure. We find the infimum of hedging risk by using a kind of min-max theorem, Also we show that this infimum is again regarded as a convex risk measure.

This paper addresses Available Bit Rate (ABR) service fairness in wide area ATM networks. In traac management, fairness is generally understood as equally sharing the available bandwidth of a link among all its contending users. The most widely used speciic fairness measure is Max-Min fairness 14]. Fairness is a very important performance measurement for ABR ow control, but no mathematical fair...

We study strategies that minimize the instability of a faulttolerant consensus system. More precisely, we find the strategy than minimizes the number of output changes over a random walk sequence of input vectors (where each component of the vector corresponds to a particular sensor reading). We analyze the case where each sensor can read three possible inputs. The proof of this result appears ...

A simple proof is presented for the min-max theorem of Lovv asz on cacti. Instead of using the result of Lovv asz on matroid parity, we shall apply twice the (conceptionally simpler) matroid intersection theorem.