Improved Approximation Algorithms for Computing k Disjoint Paths Subject to Two Constraints

For a given graph $G$ with positive integral cost and delay on edges, distinct vertices $s$ and $t$, cost bound $C\in Z^{+}$ and delay bound $D\in Z^{+}$, the $k$ bi-constraint path ($k$BCP) problem is to compute $k$ disjoint $st$-paths subject to $C$ and $D$. This problem is known NP-hard, even when $k=1$ \cite{garey1979computers}. This paper first gives a simple approximation algorithm with factor-$(2,2)$, i.e. the algorithm computes a solution with delay and cost bounded by $2*D$ and $2*C$ respectively. Later, a novel improved approximation algorithm with ratio $(1+\beta,\,\max\{2,\,1+\ln\frac{1}{\beta}\})$ is developed by constructing interesting auxiliary graphs and employing the cycle cancellation method. As a consequence, we can obtain a factor-$(1.369,\,2)$ approximation algorithm by setting $1+\ln\frac{1}{\beta}=2$ and a factor-$(1.567,\,1.567)$ algorithm by setting $1+\beta=1+\ln\frac{1}{\beta}$. Besides, by setting $\beta=0$, an approximation algorithm with ratio $(1,\, O(\ln n))$, i.e. an algorithm with only a single factor ratio $O(\ln n)$ on cost, can be immediately obtained. To the best of our knowledge, this is the first non-trivial approximation algorithm for the $k$BCP problem that strictly obeys the delay constraint.Comment: 12 page

エラスティック光ネットワークにおける変調方式を考慮した独立経路選択方式

エラスティック光ネットワークでは，スペクトルスロットと呼ばれるネットワークリソースにスペクトルの割り当てを行うことによってネットワークの管理を行っている。光パスが設定される際に，スペクトルスロットへのスペクトル割り当て要求が発生する。このとき，変調という操作が伴う。変調には様々な方式があり，それぞれ扱うことのできる経路長の上限値やスペクトルスロットの使用量が異なる。したがって，光パスが設定される際に変調方式を決定し，その変調方式に応じたスペクトルスロットの使用量が要求される。このため，光パスの経路長とスペクトルスロットの使用量は非線形関係にある。光ネットワークでは，1+1 path protectionと呼ばれる，発着ノード間において複数の独立経路を確立することによってネットワークの冗長化を図る技術がしばしば用いられている。従来の独立経路選択方式として，発着ノード間の独立経路の総経路長を最小化する，または，総ホップ数を最小化する経路選択方式がある。しかし，これらの経路選択方式では，光パスの経路長とスペクトルスロットの使用量が非線形関係にあるという理由で，必ずしも光パスを設定する際に要求されるスペクトルスロットの使用量を最小化することができるとは限らなく，これはスペクトルの利用効率を減少させる要因になる。また，既存研究に，スペクトルスロットの使用量を最小化する経路選択方式として，経路長からスペクトルスロットの使用量を求める際に，距離の刻み幅毎にスペクトルスロットの使用量を求めることにより，スペクトルスロットの使用量を最小化する方式があるが，線形化にかかる計算量が大きくなり，スケーラビリティに欠けている。本論文は，光パスの経路長と要求するスペクトルスロットの使用量が階段関数で表せることに着目し，前述した独立経路選択問題を，整数線形計画問題として定式化する。さらに，この経路選択問題がNP完全であることを証明する。性能評価により，提案方式は，従来方式と比較して，スペクトルスロットの使用量の削減効果を確認する。さらに, 計算時間の評価を行う。電気通信大学201

Algorithms for network service guarantee under minimal link usage information

One way to guaranteeing service for an application flow even if a network happens to fail is to establish a restoration path with the bandwidth that amounts to the same of the flow. If the flows can share the bandwidth for their restoration paths with others, we can reduce bandwidth consumption required for restoration. It is also required that deciding sharable bandwidth among flows should be done using controllable link information at each node. This paper proposes an algorithm to determine the sharable bandwidth among application flows given local link usage information at each node, validates the results of the algorithm and analyze the conditions required to achieve the goal by simulation.5th IFIP International Conference on Network Control & Engineering for QoS, Security and MobilityRed de Universidades con Carreras en Informática (RedUNCI

FollowMe: Efficient Online Min-Cost Flow Tracking with Bounded Memory and Computation

One of the most popular approaches to multi-target tracking is tracking-by-detection. Current min-cost flow algorithms which solve the data association problem optimally have three main drawbacks: they are computationally expensive, they assume that the whole video is given as a batch, and they scale badly in memory and computation with the length of the video sequence. In this paper, we address each of these issues, resulting in a computationally and memory-bounded solution. First, we introduce a dynamic version of the successive shortest-path algorithm which solves the data association problem optimally while reusing computation, resulting in significantly faster inference than standard solvers. Second, we address the optimal solution to the data association problem when dealing with an incoming stream of data (i.e., online setting). Finally, we present our main contribution which is an approximate online solution with bounded memory and computation which is capable of handling videos of arbitrarily length while performing tracking in real time. We demonstrate the effectiveness of our algorithms on the KITTI and PETS2009 benchmarks and show state-of-the-art performance, while being significantly faster than existing solvers

Disjoint paths in geometric graphs

Construction of the shortest paths connecting two given nodes in a geometric graph is the quintessential problem in computational geometry. We consider several variations of this problem with applications that include robotics, Geographic Information Systems, and sensor networks. The first problem we address is the development of an efficient algorithm for constructing a pair of short node-disjoint paths connecting start and target nodes. The second problem investigated is the development of efficient algorithms for constructing narrow and in-range broadcast corridors in triangulated geometric graphs. Finally, we consider the development of an approximation algorithm for constructing reduced overlap trees in three-colored geometric graphs. Theoretical analysis and a detailed experimental investigation of the proposed algorithms are also presented

One-Shot Multiple Disjoint Path Discovery Protocol (1S-MDP)

Multipath routing over disjoint paths is a classic solution to allow better resource allocation, resilience, and security. Current proposals rely on centralised computation or iterative distributed algorithms and exhibit large convergence times. We propose 1S-MDP, a distributed mechanism based on a single network exploration with concurrent path selection to discover multiple available paths among the target node and the remaining nodes in the network. The paper evaluates 1S-MDP in two different scenarios against previous solutions. We show how it reduces the convergence time by several orders of magnitude with a small decrease in the number of disjoint paths discovered.Comunidad de Madri

The complexity of finding two disjoint paths with min-max objective function

AbstractGiven a network G = (V,E) and two vertices s and t, we consider the problem of finding two disjoint paths from s to t such that the length of the longer path is minimized. The problem has several variants: The paths may be vertex-disjoint or arc-disjoint and the network may be directed or undirected. We show that all four versions as well as some related problems are strongly NP-complete. We also give a pseudo-polynomial-time algorithm for the acyclic directed case

On the benefits of backup resource sharing in transparent and opaque networks

Transparent networks promise a cost efficient solution for future core and metro networks, due to the high cost-efficiency for switching trunk traffic. Network availability is an important performance parameter for network operators, who are incorporating protection and restoration mechanisms in the network to achieve competitive advantages. This paper will focus on the reduction in Capital Expenditures (CapEx) expected from implementing protection in transparent networks. We dimension a nationwide transparent network topology for restoration and path protection mechanisms using transparent and opaque architectures. We investigate the gain through protection sharing in relation to the number of links in a meshed network and the offered load on a population of 1000 generated 2-connected planar topologies with 14 nodes. We show that the gain in a transparent network is heavily dependent on the offered load, with almost no relative gain for low load (no required parallel line systems). We also show that, for opaque networks, this relative gain by protection sharing is independent of the traffic load and shows a small dependency on the number of links in the network. The node CapEx reduction for high load is comparable to the CapEx reduction in opaque OTN systems. This is rather surprising as in OTN systems the number of transceivers and linecards and the size of the OTN switching matrix all decrease, while in transparent networks only the degree of the ROADM (number and size of WSSs in the node) decreases while the number of transponders remains the same