We consider the number of overlapping customers in several single- and multiserver queues, i.e., the number of customers whose visit to a service system at some point in time has an overlap with that of a tagged customer. Restricting ourself to ...

This paper introduces the Traveling Salesman Problem (TSP) with Backend Information Processing (bTSP), which integrates backend processing times into path planning to minimize the makespan. The study develops a mixed integer linear programming ...

This research delves into the Shannon differential entropy properties of consecutive k-out-of-n:G. Initially, an expression for the entropy of the lifetime of a consecutive k-out-of-n:G system is formulated, providing a comprehensive ...

DSatur is a widely-used heuristic algorithm for graph coloring, proposed by Daniel Brélaz in 1979. It is based on the greedy coloring approach, but selecting the next vertex to be colored from those that maximize the number of colors already used ...

Let C ⊂ R n be convex, compact, with nonempty interior and h be Legendre with domain C, continuous on C. We prove that h is Bregman if and only if it is strictly convex on C and C is a polytope. This provides insights on sequential convergence of ...

We consider cost allocation for set covering problems. We allocate as much cost to the elements (players) as possible without violating the group rationality condition, and so that the excess vector is lexicographically maximized. This happy ...

The primal separation problem for { 0 , 1 / 2 }-cuts is: Given a vertex x ˆ of the integer hull of a polytope P and some fractional point x ⁎ ∈ P, does there exist a { 0 , 1 / 2 }-cut that is tight at x ˆ and violated by x ⁎? We present two cases ...

Graphical designs are a framework for sampling and numerical integration of functions on graphs. In this note, we introduce a method to address the trade-off between graphical design sparsity and accuracy. We show how to obtain sparse graphical ...

The total matching polytope generalizes the stable set polytope and the matching polytope. In this paper, we first propose new facet-defining inequalities for the total matching polytope. We then give an exponential-sized, non-redundant ...

In the online hypergraph matching problem, hyperedges of size k over a common ground set arrive online in adversarial order. The goal is to obtain a maximum matching (disjoint set of hyperedges). A naïve greedy algorithm for this problem achieves ...

This paper proposes pandemic mitigation vaccination policies for Newfoundland and Labrador (NL) based on two compact mixed integer programming (MIP) models of the distance-based critical node detection problem (DCNDP). Our main focus is on two ...

The inverse-square law states that a source's effect is inversely proportional to the distance from that source squared. In continuous location problems, objective functions often obey the inverse-square law. This work shows that for any region ...

Circulant TSP is an intriguing special case of the Traveling Salesman Problem, whose complexity remains an often-cited open problem. In this note, we present three results: We show that circulant TSP can be efficiently solved whenever the input ...

Given k blue cities, k red cities and a 2 k × 2 k distance matrix, the task in the bipartite travelling salesman problem is to find a shortest tour which alternately visits blue and red cities. We consider the special case of Van der Veen ...

The yolk describes likely outcomes in the spatial model of voting. Martin, Nganmeni, and Tovey conjectured that given an odd number of ideal points in R k the dimension of the set of yolk centers is at most k − 2. We prove this conjecture and ...

For a connected graph G, the reciprocal degree distance ( R D D ) of the graph G is defined as; R D D ( G ) = ∑ u ≠ v deg G ⁡ ( u ) + deg G ⁡ ( v ) d G ( u , v ), where deg G ⁡ ( u ) is the degree of u in G and d G ( u , v ) is the distance ...

The effective graph resistance, also known as the Kirchhoff index, is metric that is used to quantify the robustness of a network. We show that the optimisation problem of minimizing the effective graph resistance of a graph by adding a fixed ...

Consider a gambler who on each bet either wins 1 with probability p or loses 1 with probability q = 1 − p, with the results of successive bets being independent. The gambler will stop betting when they are either up k or down k. Letting N be the ...

Many classes of two-player zero-sum stochastic games have the orderfield property; that is, if all payoffs and transitions belong to some field, so does the limit value. Is it also the case for absorbing games? No: In this note, we exhibit m × m ...

Consider a network where travel times on edges are i.i.d. over T rounds with unknown distributions. One wishes to choose departure times and routes sequentially between a given origin-destination pair across T rounds to minimize the expectations ...