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We study a delay-sensitive information flow problem where a source streams information to a sink over a directed graph G(V,E) at a fixed rate R possibly using multiple paths to minimize the maximum end-to-end delay, denoted as the Min-Max-Delay problem. Transmission over an edge incurs a constant delay within the capacity. We prove that Min-Max-Delay is weakly NP-complete, and demonstrate that it becomes strongly NP-complete if we require integer flow solution. We propose an optimal pseudo-polynomial time algorithm for Min-Max-Delay, with time complexity O(log (Nd_{max}) (N^5d_{max}^{2.5})(log R+N^2d_{max}log(N^2d_{max}))), where N = max{|V|,|E|} and d_{max} is the maximum edge delay. Besides, we show that the integrality gap, which is defined as the ratio of the maximum delay of an optimal integer flow to the maximum delay of an optimal fractional flow, could be arbitrarily large.
Asadpour, Feige, and Saberi proved that the integrality gap of the configuration LP for the restricted max-min allocation problem is at most $4$. However, their proof does not give a polynomial-time approximation algorithm. A lot of efforts have been
The max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. Each player $p$ has a non-negative value $v_{pr}$ on resource $r$. In the restricted case, we have $v_{pr}i
In this paper we present a new data structure for double ended priority queue, called min-max fine heap, which combines the techniques used in fine heap and traditional min-max heap. The standard operations on this proposed structure are also present
The restricted max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. It is NP-hard to approximate the problem to a ratio less than 2. Comparing the current best algo
In the ${-1,0,1}$-APSP problem the goal is to compute all-pairs shortest paths (APSP) on a directed graph whose edge weights are all from ${-1,0,1}$. In the (min,max)-product problem the input is two $ntimes n$ matrices $A$ and $B$, and the goal is t