We study the scaling behavior of the size of minimum dominating set (MDS) in scale-free networks, with respect to network size N and power-law exponent c, while keeping the average degree fixed. We study ensembles generated by three different network construction methods, and we use a greedy algorithm to approximate theMDS.With a structural cutoff imposed on themaximal degree kmax~ ffiffiffiffi...

We consider the following “multiway cut packing” problem in undirected graphs: given a graph G = (V,E) and k commodities, each corresponding to a set of terminals located at different vertices in the graph, our goal is to produce a collection of cuts {E1, · · · , Ek} such that Ei is a multiway cut for commodity i and the maximum load on any edge is minimized. The load on an edge is defined to b...

Let [n] = {1, 2, . . . , n} be a set with n elements, and let 2[n] denote the poset of all subsets of [n] ordered by inclusion. In other words, 2[n] is the Boolean lattice of order n or the n-dimensional hypercube. It is easy (for example using a symmetric chain decomposition [1, Theorem 3.1.1]) to find n disjoint skipless (saturated) symmetric chains of length n − 2, that is n disjoint chains ...

The aim of Network Design Problem with Vulnerability Constraints (NDPVC), introduced by Gouveia and Leitner [EJOR, 2017], is to design survivable telecommunications networks that impose length bounds on the communication paths of each commodity pair, before and after the failure of any k links. This problem was proposed as an alternative to the Hop-Constrained Survivable Network Design Problem ...

We introduce a quadratic programming framework on graphs (which incorporates MAXIMUM-CUT and MAXIMUM-INDEPENDENT-SET) and show that problems which are expressible in the framework can be solved in polynomial time on graphs without long odd cycles.

This paper proves the strong converse for any discrete memoryless network (DMN) with tight cut-set bound, i.e., whose cut-set bound is achievable. Our result implies that for any DMN with tight cut-set bound and any fixed rate tuple that resides outside the capacity region, the average error probabilities of any sequence of length-n codes operated at the rate tuple must tend to 1 as n grows. Th...

This paper proves the strong converse for any discrete memoryless network (DMN) with tight cut-set bound, i.e., whose cut-set bound is achievable. Our result implies that for any DMN with tight cut-set bound and any fixed rate tuple that resides outside the capacity region, the average error probabilities of any sequence of length-n codes operated at the rate tuple must tend to 1 as n grows. Th...

We study the problem k-SET SPLITTING in fixed parameter complexity. We show that the problem can be solved in time O∗(2.6494k), improving on the best currently known running time of O∗(8k). This is done by showing that a non-trivial instance must have a small minimal SET COVER, and using this to reduce the problem to a series of small instances of MAX SAT. We also give a linear kernel containin...

Submodular functions are common in combinatorics; examples include the cut capacity function of a graph and the rank function of a matroid. The submodular function minimization problem generalizes the classical minimum cut problem and also contains a number of other combinatorial optimization problems as special cases. In this thesis, we study submodular function minimization and two related pr...

We investigate an algebraic approach to a conjecture of Conforti and Cornuéjols by examining associated primes of square-free monomial ideals. The conjecture states that a clutter C has the max-flow min-cut (MFMC) property if and only if it has the packing property. We show that if a minimal counterexample C to this conjecture exists then C cannot be unmixed. It is known that C satisfies MFMC i...