We provide a new combinatorial approach to study the minimal free resolutions of edge ideals, that is, quadratic square-free monomial ideals. With this method we can recover most of the known results on resolutions of edge ideals with fuller generality, and at the same time, obtain new results. Past investigations on the resolutions of edge ideals usually reduced the problem to computing the di...

We study the polyhedra of splittable and unsplittable single arc–set relaxations of multicommodity flow capacitated network design problems. We investigate the optimization problems over these sets and the separation and lifting problems of valid inequalities for them. In particular, we give a linear–time separation algorithm for the residual capacity inequalities [19] and show that the separat...

We consider a generalization of the unsplittable maximum two-commodity flow problem on undirected graphs where each commodity i ∈ {1,2} can be split into a bounded number ki of equally-sized chunks that can be routed on different paths. We show that in contrast to the single-commodity case this problem is NP-hard, and hard to approximate to within a factor of α > 1/2. We present a polynomial ti...

In sequential hypothesis testing, Generalized Binary Search (GBS) greedily chooses the test with the highest information gain at each step. It is known that GBS obtains the gold standard query cost of O(log n) for problems satisfying the k-neighborly condition, which requires any two tests to be connected by a sequence of tests where neighboring tests disagree on at most k hypotheses. In this p...

We consider the Robust Network Loading problem with splittable flows and demands that belong to the budgeted uncertainty set. Four routing schemes are investigated: static, volume, affine and dynamic. First, following what done for static and dynamic routing, we derive capacity formulation for affine and volume routing. This is done using a Benders reformulation approach. Then, we introduce the...

IEEE 802.16, also known as WiMAX (Worldwide Inter-operability for Microwave Access), is a new wireless access technology for current increasing demand of wireless high-speed broadband service. Efficient and effective deployment of such a network to service an area of users with certain traffic demands is an important network planning problem. This network planning can be formulated in a similar...

We study a non-cooperative two-sided facility location game in which facilities and clients behave strategically. This is contrast to many other games simply visit their closest facility. Facility agents select on graph open attract as much purchasing power possible, while client choose patronize by strategically distributing order minimize total waiting time. Here, the time of depends its rece...

The main result of the paper is a description of the maximal ideals in the modular group algebras of the finitary symmetric and alternating groups (provided the characteristic p of the ground field is greater than 2). For the symmetric group there are exactly p − 1 such ideals and for the alternating group there are (p − 1)/2 of them. The description is obtained in terms of the annihilators of ...

In this paper we study the network design arc set with variable upper bounds. This set appears as a common substructure of many network design problems and is a relaxation of several fundamental mixed-integer sets studied earlier independently. In particular, the splittable flow arc set, the unsplittable flow arc set, the single node fixed-charge flow set, and the binary knapsack set are facial...

We present several examples of programs which ee-ciently monitor the answers from queries performed on data structures to determine if any errors are present. Our paper includes the rst eecient on-line error monitor for a data structure designed to perform nearest neighbor queries. Applications of nearest neighbor queries are extensive and include learning, categorization, speech processing , a...